A001748 -id:A001748 - cp's OEIS frontend

A377872 Numbers k for which A276085(k) is a multiple of 27, where A276085 is fully additive with a(p) = p#/p.

1, 55, 95, 115, 155, 174, 187, 203, 232, 265, 282, 297, 323, 325, 329, 335, 376, 391, 396, 438, 462, 474, 511, 513, 515, 527, 528, 539, 553, 584, 606, 616, 621, 632, 649, 654, 678, 684, 704, 707, 745, 763, 791, 798, 808, 828, 837, 872, 901, 904, 906, 912, 913, 931, 966, 978, 1002, 1057, 1064, 1073, 1074, 1075, 1104, 1105

Offset: 1

Antti Karttunen, Nov 10 2024

nonn

A multiplicative semigroup; if m and n are in the sequence then so is m*n.
From Antti Karttunen, Nov 17 2024: (Start)
Question: What is the asymptotic density of this sequence? There are 1, 3, 56, 484, 4899, 50034, 508254 terms <= 10^k, for k=1..7. See also questions in A377869 and in A377878.
If 3*x is a term, then 4*x is also a term, and vice versa.
Contains no even semiprimes (A100484), semiprimes of the form 3*prime (A001748), nor terms of the form 4*prime (A001749).
(End)

Antti Karttunen, Table of n, a(n) for n = 1..12000
Index entries for sequences related to primorial numbers

Cf. A276085, A377869, A377876, A377878.
Subsequence of A339746, and of A377873.
Cf. also A369007, A377875.

isA377872(n) = { my(m=27, f = factor(n), pr=1, i=1, s=0); for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= Mod(prime(i),m); i++); s += f[k, 2]*pr); (0==lift(s)); };

{k such that Sum e*A377876(A000720(p)-1) == 0 (mod 27), when k = Product(p^e)}.

A023883 Nonprimes whose average of divisors is an integer.

Original entry on oeis.org

1, 6, 14, 15, 20, 21, 22, 27, 30, 33, 35, 38, 39, 42, 44, 45, 46, 49, 51, 54, 55, 56, 57, 60, 62, 65, 66, 68, 69, 70, 77, 78, 85, 86, 87, 91, 92, 93, 94, 95, 96, 99, 102, 105, 110, 111, 114, 115, 116, 118, 119, 123, 125, 126, 129, 132, 133, 134, 135, 138

Offset: 1

Olivier Gérard

nonn

From Bernard Schott, Mar 27 2021: (Start)
Some subsequences of these nonprimes arithmetic numbers.
  - Squares of primes of the form 6k+1 (A002476).
  - Cubes of odd primes (A030078 \ {8}).
  - Semiprimes 2*p where prime p is of the form 4k+3 (A002145).
  - Semiprimes 3*p where p prime <> 3 (A001748 \ {9}).
  - Integers 4*p where prime p is of the form 6k-1 (A007528). (End)

			Sigma(22) = 36, tau(22) = 4, sigma(22)/tau(2) = 9, 22 is not prime, hence 22 belongs to this sequence.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (term 1..1000 from Paolo P. Lava)

Intersection of A003601 and A018252.
Equals A003601 \ A000040.
Cf. A000005 (tau), A000203 (sigma).
Cf. A001748, A002145, A002476, A007528, A030078.

Select[{Mean[Divisors[#]], #}& /@ Select[Range[140], !PrimeQ[#]&], IntegerQ[#[[1]]]&][[All, 2]] (* Jean-François Alcover, Oct 31 2017 *)

A253046 An involution of the natural numbers: if n = 2p_i then replace n with 3p_{i+1}, and conversely if n = 3p_i then replace n with 2p_{i-1}, where p_i denotes the i-th prime.

Original entry on oeis.org

1, 2, 3, 9, 5, 15, 7, 8, 4, 21, 11, 12, 13, 33, 6, 16, 17, 18, 19, 20, 10, 39, 23, 24, 25, 51, 27, 28, 29, 30, 31, 32, 14, 57, 35, 36, 37, 69, 22, 40, 41, 42, 43, 44, 45, 87, 47, 48, 49, 50, 26, 52, 53, 54, 55, 56, 34, 93, 59, 60, 61, 111, 63, 64, 65, 66, 67

Offset: 1

N. J. A. Sloane, Dec 26 2014

nonn

a(m) != m iff m is a term of A253106, i.e., a semiprime divisible by 2 or 3; a(A100484(n)) > A100484(n); a(A001748(n)) < A001748(n). - Reinhard Zumkeller, Dec 26 2014

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
A. B. Frizell, Certain non-enumerable sets of infinite permutations. Bull. Amer. Math. Soc. 21 (1915), no. 10, 495-499.
Index entries for sequences that are permutations of the natural numbers

Cf. A064614, A251561, A020639, A049084, A000040, A253106, A001748, A100484.

a253046 n | i == 0 || p > 3 = n
          | p == 2          = 3 * a000040 (i + 1)
          | otherwise       = 2 * a000040 (i - 1)
            where i = a049084 (div n p);  p = a020639 n
-- Reinhard Zumkeller, Dec 26 2014

a253046[n_] := Block[{f},
  f[x_] := Which[PrimeQ[x/2], 3 NextPrime[x/2],
    PrimeQ[x/3], 2 NextPrime[x/3, -1],
True, x];Array[f, n]]; a253046[67] (* Michael De Vlieger, Dec 27 2014 *)

from sympy import isprime, nextprime, prevprime
def A253046(n):
    q2, r2 = divmod(n,2)
    if not r2 and isprime(q2):
        return 3*nextprime(q2)
    else:
        q3, r3 = divmod(n,3)
        if not r3 and isprime(q3):
            return 2*prevprime(q3)
        return n # Chai Wah Wu, Dec 27 2014

A264102 Numbers n with the property that the symmetric representation of sigma(n) has four parts, each of width one.

Original entry on oeis.org

21, 27, 33, 39, 51, 55, 57, 65, 69, 85, 87, 93, 95, 111, 115, 119, 123, 125, 129, 133, 141, 145, 155, 159, 161, 177, 183, 185, 201, 203, 205, 213, 215, 217, 219, 230, 235, 237, 249, 250, 253, 259, 265, 267, 287, 290, 291, 295, 301, 303, 305, 309, 310, 319, 321, 327, 329, 335

Offset: 1

Hartmut F. W. Hoft, Nov 03 2015

The areas of the first two regions are (2^(m+1) - 1) * (p * q + 1) / 2 and (2^(m+1) - 1) * (p + q) / 2, respectively. Twice their sum equals sigma(n) = (2^(m+1) - 1) * (p + 1) * (q + 1).

For a proof of the formula for this sequence see the link.

			65 = 5*13 is in the sequence since m = 0 and 2 < 5 < 10 < 13. The first two regions in the symmetric representation of sigma(65) = 84 start with legs 1 and 5 of the Dyck path and have areas 33 and 9, respectively.
406 = 2*7*29 is in the sequence since m=1 and 4 < 7 < 28 < 29. The first two regions in the symmetric representation of sigma(406) = 720 start with legs 1 and 7 and have areas 306 and 54, respectively. Note also that 406 is a triangular number and the middle two regions meet at the center of the Dyck path.
One case in the formula for the sequence is the 3-parameter expression n = 2^m * p * q with p and q distinct primes satisfying the stated conditions. That subsequence can be visualized as a skew tetrahedron since the start of each "line" on an irregular "triangular" side of the "tetrahedron" is determined by a different prime number and each layer is determined by a different power of two. Below are the first three layers with primes p designating columns and primes q rows.
m=0| 3    5    7    11   13
-----------------------------
7  | 21
11 | 33   55
13 | 39   65
17 | 51   85   119
19 | 57   95   133
23 | 69   115  161  253
29 | 87   145  203  319  377
31 | 93   155  217  341  403
37 | 111  185  259  407  481
41 | 123  205  287  451  533
...
89 | 267  445  623  979  1157
...
Column 1 is A001748 except for the first three terms and column 2 is A001750 except for the first four terms in the two resepctive sequences.
m=1| 3    5    7    11   13
-------------------------------
23 |     230
29 |     290  406
31 |     310  434
37 |     370  518
41 |     410  574
43 |     430  602
47 |     470  658  1034
53 |     530  742  1166  1378
...
89 |     890  1246 1958  2314
...
m=2| 3    5    7    11   13
-------------------------------
89 |               3916
97 |               4268
101|               4444
103|               4532
107|               4708  5564
109|               4796  5668
...
The fourth layer for m = 3 starts with number 37672 in column p = 17 and row q = 277.
The subsequence of the 2-parameter case n = 2^m * p^3 with 2^(m+1) < p gives rise to the following irregular triangle:
p\m| 0      1       2       3
----------------------------------
3  | 27
5  | 125    250
7  | 343    686
11 | 1331   2662    5324
13 | 2197   4394    8788
17 | 4913   9826    19652   39304
19 | 6859   13718   27436   54872
23 | 12167  24334   48668   97336
29 | 24389  48778   97556   195112
...
The first column in this triangle is A030078 except for the first term and the second column is A172190 except for the first two terms respectively in the two sequences.

Hartmut F. W. Hoft, Diagram of symmetric representations of sigma
Hartmut F. W. Hoft, Proof of formula for 4 regions of width 1

Cf. A001748, A001750, A030078, A172190.
For symmetric representation of sigma: A235791, A236104, A237270, A237271, A237591, A237593, A241008, A246955.
Subsequence of A280107.

mpStalk[m_, p_, bound_] := Module[{q=NextPrime[2^(m+1)*p], list={}}, While[2^m*p*q<=bound, AppendTo[list, 2^m*p*q]; q=NextPrime[q]]; If[2^m*p^3<=bound, AppendTo[list, 2^m*p^3]]; list]
mTriangle[m_, bound_] := Module[{p=NextPrime[2^(m+1)], list={}}, While[2^m*p*NextPrime[2^(m+1)*p]<=bound, list=Union[list, mpStalk[m, p, bound]]; p=NextPrime[p]]; list]
(* 2^(4m+3)<=bound is a simpler test, but computes some empty stalks *)
a264102[bound_] := Module[{m=0, list={}}, While[2^m*NextPrime[2^(m+1)]*NextPrime[2^(m+1)*NextPrime[2^(m+1)]]<=bound, list=Union[list, mTriangle[m, bound]]; m++]; list]
a264102[335] (* data *)

n = 2^m * p * q where m >= 0, p > 2 is prime, 2^(m+1) < p < 2^(m+1) * p < q, and either q is prime or q = p^2.

A272214 Square array read by antidiagonals upwards in which T(n,k) is the product of the n-th prime and the sum of the divisors of k, n >= 1, k >= 1.

Original entry on oeis.org

2, 3, 6, 5, 9, 8, 7, 15, 12, 14, 11, 21, 20, 21, 12, 13, 33, 28, 35, 18, 24, 17, 39, 44, 49, 30, 36, 16, 19, 51, 52, 77, 42, 60, 24, 30, 23, 57, 68, 91, 66, 84, 40, 45, 26, 29, 69, 76, 119, 78, 132, 56, 75, 39, 36, 31, 87, 92, 133, 102, 156, 88, 105, 65, 54, 24, 37, 93, 116, 161, 114, 204, 104, 165, 91, 90, 36, 56

Offset: 1

Omar E. Pol, Apr 28 2016

From Omar E. Pol, Dec 21 2021: (Start)
Also triangle read by rows: T(n,j) = A000040(n-j+1)*A000203(j), 1 <= j <= n.
For a visualization of T(n,j) first consider a tower (a polycube) in which the terraces are the symmetric representation of sigma(j), for j = 1 to n, starting from the top, and the heights of the terraces are the first n prime numbers respectively starting from the base. Then T(n,j) can be represented with a set of A237271(j) right prisms of height A000040(n-j+1) since T(n,j) is also the total number of cubes that are exactly below the parts of the symmetric representation of sigma(j) in the tower.
The sum of the n-th row of triangle is A086718(n) equaling the volume of the tower whose largest side of the base is n and its total height is the n-th prime.
The tower is an member of the family of the stepped pyramids described in A245092 and of the towers described in A221529. That is an infinite family of symmetric polycubes whose volumes represent the convolution of A000203 with any other integer sequence. (End)

			The corner of the square array begins:
   2,  6,   8,  14,  12,  24,  16,  30,  26,  36, ...
   3,  9,  12,  21,  18,  36,  24,  45,  39,  54, ...
   5, 15,  20,  35,  30,  60,  40,  75,  65,  90, ...
   7, 21,  28,  49,  42,  84,  56, 105,  91, 126, ...
  11, 33,  44,  77,  66, 132,  88, 165, 143, 198, ...
  13, 39,  52,  91,  78, 156, 104, 195, 169, 234, ...
  17, 51,  68, 119, 102, 204, 136, 255, 221, 306, ...
  19, 57,  76, 133, 114, 228, 152, 285, 247, 342, ...
  23, 69,  92, 161, 138, 276, 184, 345, 299, 414, ...
  29, 87, 116, 203, 174, 348, 232, 435, 377, 522, ...
  ...
From _Omar E. Pol_, Dec 21 2021: (Start)
Written as a triangle the sequence begins:
   2;
   3,  6;
   5,  9,  8;
   7, 15, 12,  14;
  11, 21, 20,  21,  12;
  13, 33, 28,  35,  18,  24;
  17, 39, 44,  49,  30,  36, 16;
  19, 51, 52,  77,  42,  60, 24,  30;
  23, 57, 68,  91,  66,  84, 40,  45, 26;
  29, 69, 76, 119,  78, 132, 56,  75, 39, 36;
  31, 87, 92, 133, 102, 156, 88, 105, 65, 54, 24;
...
Row sums give A086718. (End)

Ivan Neretin, Table of n, a(n) for n = 1..8128

Rows 1-4 of the square array: A074400, A272027, A274535, A319527.
Columns 1-5 of the square array: A000040, A001748, A001749, A138636, A272470.
Main diagonal of the square array gives A272211.
Cf. A086718 (antidiagonal sums of the square array, row sums of the triangle).
Cf. A000203, A221529, A237270, A237271, A237593, A245092, A272173, A272400, A274824.

Table[Prime[#] DivisorSigma[1, k] &@(n - k + 1), {n, 12}, {k, n}] // Flatten (* Michael De Vlieger, Apr 28 2016 *)

T(n,k) = prime(n)*sigma(k) = A000040(n)*A000203(k), n >= 1, k >= 1.

T(n,k) = A272400(n+1,k).

A143215 a(n) = prime(n) * Sum_{i=1..n} prime(i).

Original entry on oeis.org

4, 15, 50, 119, 308, 533, 986, 1463, 2300, 3741, 4960, 7289, 9758, 12083, 15416, 20193, 25960, 30561, 38056, 45369, 51976, 62489, 72542, 85707, 102820, 117261, 130192, 146697, 161320, 180009, 218440, 242481, 272356, 295653, 339124, 366477

Offset: 1

Gary W. Adamson, Jul 30 2008

nonn

Row sums of triangle A087112.

Sum of semiprimes (A001358) with greater prime factor prime(n). - Gus Wiseman, Dec 06 2020

			The series begins (4, 15, 50, 119, 308,...) since the primes = (2, 3, 5, 7, 11,...) and partial sum of primes = (2, 5, 10, 17, 28,...).
a(5) = 308 = 11 * 28.
a(4) = 119 = sum of row 4 terms of triangle A087112: (14 + 21 + 35 + 49).

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Row sums of A087112.
The squarefree version is A339194, row sums of A339116.
Semiprimes grouped by weight are A338904, with row sums A024697.
Squarefree semiprimes grouped by weight are A338905, with row sums A025129.
Squarefree numbers grouped by greatest prime factor are A339195, with row sums A339360.
A001358 lists semiprimes.
A006881 lists squarefree semiprimes.
A332765 is the greatest semiprime of weight n.
A338898/A338912/A338913 give the prime indices of semiprimes.
A338899/A270650/A270652 give the prime indices of squarefree semiprimes.
Cf. A000040, A001222, A001748, A007504, A014342, A098350, A100484, A168472, A319613, A339003, A339114/A339115.

a143215 n = a000040 n * a007504 n  -- Reinhard Zumkeller, Nov 25 2012

A143215:= func< n | NthPrime(n)*(&+[NthPrime(j): j in [1..n]]) >;
[A143215(n): n in [1..50]]; // G. C. Greubel, Aug 27 2024

A143215:=n->ithprime(n)*sum(ithprime(i), i=1..n); seq(A143215(n), n=1..50); # Wesley Ivan Hurt, Mar 26 2014

Table[Prime[n]*Sum[Prime[i], {i, n}], {n, 50}] (* Wesley Ivan Hurt, Mar 26 2014 *)

a(n) = prime(n)*vecsum(primes(n)); \\ Michel Marcus, Jun 15 2024

def A143215(n): return nth_prime(n)*sum(nth_prime(j) for j in range(1,n+1))
[A143215(n) for n in range(1,51)] # G. C. Greubel, Aug 27 2024

a(n) = A000040(n) * A007504(n).

More terms from Vladimir Joseph Stephan Orlovsky, Sep 21 2009

A098742 Number of indecomposable set partitions of [1..n] without singletons.

Original entry on oeis.org

0, 0, 1, 1, 3, 9, 33, 135, 609, 2985, 15747, 88761, 531561, 3366567, 22462017, 157363329, 1154257683, 8841865833, 70573741857, 585753925047, 5046128460801, 45044554041897, 416005748766771, 3969321053484921, 39077616720410409

Offset: 0

Don Knuth, Oct 01 2004

After a(3) = 1, always divisible by 3. a(n) is 3 times a prime (A001748) when n = 5, 6, 11, 14, 15, 16, 19. - Jonathan Vos Post, Jun 22 2008

			a(5)=9 because of the set partitions 135|24, 134|25, 125|34, 145|23, 15|234, 13|245, 124|35, 12345, 14|235. [Puttenham missed the last of these.]

D. E. Knuth, TAOCP, Vol. 4, Section 7.2.1.7, Problem 26.
George Puttenham, The Arte of English Poesie (1589), page 72, can be said to have stated the problem; but he omitted one case for n=5 and 22 cases for n=6, so he must have had other constraints in mind!

Alois P. Heinz, Table of n, a(n) for n = 0..500

Cf. A000296, A074664, A001748, A008585.

F:= proc(n) option remember; convert(series(1 -1/add(coeff(series(exp(exp(x)-1), x,n+1), x,j)*j!*x^j, j=0..n), x,n+1), polynom) end: a:= n-> coeff(series(x*F(n)/(1+x-F(n)), x,n+1), x,n): seq(a(n), n=0..24); # Alois P. Heinz, Sep 05 2008

f[n_] := f[n] = Normal[ Series[ 1-1/Sum[ SeriesCoefficient[ Series[ Exp[Exp[x] - 1], {x, 0, n + 1}], {x, 0, j}]*j!*x^j, {j, 0, n}], {x, 0, n + 1}]]; a[0] = 0; a[n_] := SeriesCoefficient[ Series[ x*(f[n]/(1 + x - f[n])), {x, 0, n + 1}], {x, 0, n}]; Table[a[n], {n, 0, 24}] (* Jean-François Alcover, translated from Maple *)

def A098742_list(dim):
    T = matrix(ZZ,dim,dim)
    for n in range(dim): T[n,n] = 1
    for n in (1..dim-1):
        for k in (0..n-1):
            T[n,k] = T[n-1,k-1]+(k+1)*T[n-1,k]+(k+2)*T[n-1,k+1]
    return [0,0]+list(T.column(0))
A098742_list(23) # - Peter Luschny, Sep 20 2012

If f(z) is the generating function for A074664, then a(z)=zf(z)/(1+z-f(z)).
Also, if g(z) is the generating function for A000296, then a(z) = 1-1/g(z).
O.g.f.: x^2/(1-x-2*x^2/(1-2*x-3*x^2/(1-3*x-4*x^2/(1-... -n*x-(n+1)*x^2/(1- ...)))))) (continued fraction). - Paul D. Hanna, Jan 17 2006
From Sergei N. Gladkovskii, Sep 20 2012, Nov 04 2012, Feb 04 2013, Feb 23 2013, Apr 18 2013, May 12 2013: (Start) Continued fractions:
G.f.: -x + 2*x/E(0) where E(k)= 1 + 1/(1 + 2*x/(1 - 2*(k+2)*x/E(k+1))).
G.f.: 1 - x*U(0,1/x) where U(k,x)= x - k - (k+1)/U(k+1,x).
G.f.: (1+x)*x/G(0) - x where G(k) = 1 + x - x*(k+1)/(1 - x/G(k+1)).
G.f.: x/Q(0) - x where Q(k)= 1 + x/(x*k-x-1)/Q(k+1).
G.f.: 1 - Q(0) where Q(k)= 1 + x - x/(1 - x*(k+1)/Q(k+1)).
G.f.: 1-x-1/Q(0) where Q(k)= 1 + x/(1 - x - x*(k+1)/(x + 1/Q(k+1))). (End)

More terms from Vladeta Jovovic, Oct 21 2004

A098764 a(n) = 3p - q where p and q are consecutive primes.

Original entry on oeis.org

3, 4, 8, 10, 20, 22, 32, 34, 40, 56, 56, 70, 80, 82, 88, 100, 116, 116, 130, 140, 140, 154, 160, 170, 190, 200, 202, 212, 214, 212, 250, 256, 272, 268, 296, 296, 308, 322, 328, 340, 356, 352, 380, 382, 392, 386, 410, 442, 452, 454, 460, 476, 472, 496, 508, 520

Offset: 1

Giovanni Teofilatto, Sep 30 2004

Except for the initial term, a(n)=={2, 4} mod 6.

Not monotonic: a(29) = 214 > 212 = a(30), a(33) = 272 > 268 = a(34), etc. - Charles R Greathouse IV, Jun 03 2013

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A000040, A001043, A001223, A001748, A047235, A100021.

ListConvolve[{-1,3},Prime[Range[100]]] (* Paolo Xausa, Nov 02 2023 *)

a(n) = 3*prime(n) - prime(n+1) \\ Michel Marcus, Jun 03 2013

a(n) = A001043(n) - 2*A001223(n).
a(n) = 3*A000040(n)-A000040(n+1) = A001748(n)-A000040(n+1) = A001747(n+1)-A001223(n). - R. J. Mathar, Apr 22 2010
a(n) ~ 2n log n. - Charles R Greathouse IV, Jun 03 2013
a(n) = A100021(n) + 3. - Hugo Pfoertner, Nov 02 2023
a(n) = A062234(n) + A000040(n). - Anthony S. Wright, Feb 19 2024

Corrected (116 duplicated) by R. J. Mathar, Apr 22 2010

A112773 3 together with primes multiplied by 3.

Original entry on oeis.org

3, 6, 9, 15, 21, 33, 39, 51, 57, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 201, 213, 219, 237, 249, 267, 291, 303, 309, 321, 327, 339, 381, 393, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633, 669, 681, 687, 699, 717, 723, 753

Offset: 1

Jonathan Vos Post and Ray Chandler, Oct 15 2005

3 times the noncomposite numbers (see formula). Also column 2 of A272400. - Omar E. Pol, Apr 29 2016

G. C. Greubel, Table of n, a(n) for n = 1..1000

Essentially the same as A001748.

Cf. A000040, A001747, A008578, A008585, A046315.

Insert[Table[3Prime[n], {n, 1, 60}], 3, 1] (* Stefan Steinerberger, Mar 30 2006 *)

a(n) = 3*A008578(n). - Omar E. Pol, Jan 31 2012

Edited by N. J. A. Sloane, Apr 28 2008 at the suggestion of Alexander R. Povolotsky

A176003 a(n) = 3*(n-th noncomposite number) - 2.

Original entry on oeis.org

1, 4, 7, 13, 19, 31, 37, 49, 55, 67, 85, 91, 109, 121, 127, 139, 157, 175, 181, 199, 211, 217, 235, 247, 265, 289, 301, 307, 319, 325, 337, 379, 391, 409, 415, 445, 451, 469, 487, 499, 517, 535, 541, 571, 577, 589, 595, 631, 667, 679, 685, 697, 715, 721, 751

Offset: 1

Juri-Stepan Gerasimov, Apr 11 2010

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Barry Brent, On the constant terms of certain meromorphic modular forms for Hecke groups, arXiv:2212.12515 [math.NT], 2022.
Barry Brent, On the Constant Terms of Certain Laurent Series, Preprints (2023) 2023061164.

Cf. A001748, A008578.

[3*NthPrime(n)-2: n in [0..58]]; // Vincenzo Librandi, Dec 08 2015

Join[{1}, Table[3 Prime[n] - 2, {n, 60}]] (* Vincenzo Librandi, Dec 08 2015 *)

a(n) = 3*A008578(n) - 2. - R. J. Mathar, Apr 16 2010

Entries checked by R. J. Mathar, Apr 16 2010

cp's OEIS Frontend

A377872 Numbers k for which A276085(k) is a multiple of 27, where A276085 is fully additive with a(p) = p#/p.

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A023883 Nonprimes whose average of divisors is an integer.

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A253046 An involution of the natural numbers: if n = 2*p_i then replace n with 3*p_{i+1}, and conversely if n = 3*p_i then replace n with 2*p_{i-1}, where p_i denotes the i-th prime.

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A264102 Numbers n with the property that the symmetric representation of sigma(n) has four parts, each of width one.

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A272214 Square array read by antidiagonals upwards in which T(n,k) is the product of the n-th prime and the sum of the divisors of k, n >= 1, k >= 1.

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A143215 a(n) = prime(n) * Sum_{i=1..n} prime(i).

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A098742 Number of indecomposable set partitions of [1..n] without singletons.

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A253046 An involution of the natural numbers: if n = 2p_i then replace n with 3p_{i+1}, and conversely if n = 3p_i then replace n with 2p_{i-1}, where p_i denotes the i-th prime.