A052147 -id:A052147 - cp's OEIS frontend

A008472 Sum of the distinct primes dividing n.

0, 2, 3, 2, 5, 5, 7, 2, 3, 7, 11, 5, 13, 9, 8, 2, 17, 5, 19, 7, 10, 13, 23, 5, 5, 15, 3, 9, 29, 10, 31, 2, 14, 19, 12, 5, 37, 21, 16, 7, 41, 12, 43, 13, 8, 25, 47, 5, 7, 7, 20, 15, 53, 5, 16, 9, 22, 31, 59, 10, 61, 33, 10, 2, 18, 16, 67, 19, 26, 14, 71, 5, 73

Offset: 1

Olivier Gérard

Sometimes called sopf(n).
Sum of primes dividing n (without repetition) (compare A001414).
Equals A051731 * A061397 = inverse Mobius transform of [0, 2, 3, 0, 5, 0, 7, ...]. - Gary W. Adamson, Feb 14 2008
Equals row sums of triangle A143535. - Gary W. Adamson, Aug 23 2008
a(n) = n if and only if n is prime. - Daniel Forgues, Mar 24 2009
a(n) = n is a new record if and only if n is prime. - Zak Seidov, Jun 27 2009
a(A001043(n)) = A191583(n);
For n > 0: a(A000079(n)) = 2, a(A000244(n)) = 3, a(A000351(n)) = 5, a(A000420(n)) = 7;
a(A006899(n)) <= 3; a(A003586(n)) = 5; a(A033846(n)) = 7; a(A033849(n)) = 8; a(A033847(n)) = 9; a(A033850(n)) = 10; a(A143207(n)) = 10. - Reinhard Zumkeller, Jun 28 2011
For n > 1: a(n) = Sum(A027748(n,k): 1 <= k <= A001221(n)). - Reinhard Zumkeller, Aug 27 2011
If n is the product of twin primes (A037074), a(n) = 2*sqrt(n+1) = sqrt(4n+4). - Wesley Ivan Hurt, Sep 07 2013
From Wilf A. Wilson, Jul 21 2017: (Start)
a(n) + 2, n > 2, is the number of maximal subsemigroups of the monoid of orientation-preserving or -reversing mappings on a set with n elements.
a(n) + 3, n > 2, is the number of maximal subsemigroups of the monoid of orientation-preserving or -reversing partial mappings on a set with n elements.
(End)
The smallest m such that a(m) = n, or 0 if no such number m exists is A064502(n). The only integers that are not in the sequence are 1, 4 and 6. - Bernard Schott, Feb 07 2022

			a(18) = 5 because 18 = 2 * 3^2 and 2 + 3 = 5.
a(19) = 19 because 19 is prime.
a(20) = 7 because 20 = 2^2 * 5 and 2 + 5 = 7.

Daniel Forgues, Table of n, a(n) for n = 1..100000 (first 10000 terms from Franklin T. Adams-Watters)
Johann Bartel, R. K. Bhaduri, Matthias Brack, and M. V. N. Murthy, On the asymptotic prime partitions of integers, arXiv:1609.06497 [math-ph], 2017.
James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017. [_Wilf A. Wilson_, Jul 21 2017]

First difference of A024924.
Cf. A001414 (sopfr), A001222, A051731, A061397, A064502, A085020, A143535.
Sum of the k-th powers of the primes dividing n for k=0..10 : A001221 (k=0), this sequence (k=1), A005063 (k=2), A005064 (k=3), A005065 (k=4), A351193 (k=5), A351194 (k=6), A351195 (k=7), this sequence (k=8), A351197 (k=9), A351198 (k=10).
Cf. A010051.

a008472 = sum . a027748_row  -- Reinhard Zumkeller, Mar 29 2012

[n eq 1 select 0 else &+[p[1]: p in Factorization(n)]: n in [1..100]]; // Vincenzo Librandi, Jun 24 2017

A008472 := n -> add(d, d = select(isprime, numtheory[divisors](n))):
seq(A008472(i), i = 1..40); # Peter Luschny, Jan 31 2012
A008472 := proc(n)
        add( d, d= numtheory[factorset](n)) ;
end proc: # R. J. Mathar, Jul 08 2012

Prepend[Array[Plus @@ First[Transpose[FactorInteger[#]]] &, 100, 2], 0]
Join[{0}, Rest[Total[Transpose[FactorInteger[#]][[1]]]&/@Range[100]]] (* Harvey P. Dale, Jun 18 2012 *)
(* Requires version 7.0+ *) Table[DivisorSum[n, # &, PrimeQ[#] &], {n, 75}] (* Alonso del Arte, Dec 13 2014 *)
Table[Sum[p, {p, Select[Divisors[n], PrimeQ]}], {n, 1, 100}] (* Vaclav Kotesovec, May 20 2020 *)

sopf(n) = local(fac=factor(n)); sum(i=1,matsize(fac)[1],fac[i,1])

vector(100,n,vecsum(factor(n)[,1]~)) \\ Derek Orr, May 13 2015

A008472(n)=vecsum(factor(n)[,1]) \\ M. F. Hasler, Jul 18 2015

from sympy import primefactors
def A008472(n): return sum(primefactors(n)) # Chai Wah Wu, Feb 03 2022

def A008472(n):
    return add(d for d in divisors(n) if is_prime(d))
print([A008472(i) for i in (1..40)]) # Peter Luschny, Jan 31 2012

[sum(prime_factors(n)) for n in range(1,74)] # Giuseppe Coppoletta, Jan 19 2015

Let n = Product_j prime(j)^k(j) where k(j) >= 1, then a(n) = Sum_j prime(j).
Additive with a(p^e) = p.
G.f.: Sum_{k >= 1} prime(k)*x^prime(k)/(1-x^prime(k)). - Franklin T. Adams-Watters, Sep 01 2009
L.g.f.: -log(Product_{k>=1} (1 - x^prime(k))) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 06 2017
Dirichlet g.f.: primezeta(s-1)*zeta(s). - Benedict W. J. Irwin, Jul 11 2018
a(n) = Sum_{p|n, p prime} p. - Wesley Ivan Hurt, Feb 04 2022
From Bernard Schott, Feb 07 2022: (Start)
For n > 0: a(A001020(n)) = 11, a(A001022(n)) = 13, a(A001026(n)) = 17, a(A001029(n)) = 19, a(A009967(n)) = 23, a(A009973(n)) = 29, a(A009975(n)) = 31, a(A009981(n)) = 37, a(A009985(n)) = 41, a(A009987(n)) = 43, a(A009991(n)) = 47.
For p odd prime, a(2*p) = p+2 <==> a(A100484(n)) = A052147(n) for n > 1. (End)
a(n) = Sum_{d|n} d * c(d), where c = A010051. - Wesley Ivan Hurt, Jun 22 2024

A018818 Number of partitions of n into divisors of n.

Original entry on oeis.org

1, 2, 2, 4, 2, 8, 2, 10, 5, 11, 2, 45, 2, 14, 14, 36, 2, 81, 2, 92, 18, 20, 2, 458, 7, 23, 23, 156, 2, 742, 2, 202, 26, 29, 26, 2234, 2, 32, 30, 1370, 2, 1654, 2, 337, 286, 38, 2, 9676, 9, 407, 38, 454, 2, 3132, 38, 3065, 42, 47, 2, 73155, 2, 50, 493, 1828, 44, 5257, 2, 740, 50, 5066

Offset: 1

David W. Wilson

From Reinhard Zumkeller, Dec 11 2009: (Start)
For odd primes p: a(p^2) = p + 2; for n > 1: a(A001248(n)) = A052147(n);
For odd primes p > 3, a(3*p) = 2*p + 4; for n > 2: a(A001748(n)) = A100484(n) + 4. (End)
From Matthew Crawford, Jan 19 2021: (Start)
For a prime p, a(p^3) = (p^3 + p^2 + 2*p + 4)/2;
For distinct primes p and q, a(p*q) = (p+1)*(q+1)/2 + 2. (End)

			The a(6) = 8 representations of 6 are 6 = 3 + 3 = 3 + 2 + 1 = 3 + 1 + 1 + 1 = 2 + 2 + 2 = 2 + 2 + 1 + 1 = 2 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 + 1.

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
Douglas Bowman et al., Problem 6640: Partitions of n into parts which are divisors of n, American Mathematical Monthly, 99(3) (1992), 276-277.
Hansraj Gupta, Partitions of n into divisors of m, Indian J. Pure Appl. Math., 6(11) (1975), 1276-1286.
Hansraj Gupta, Partitions of n into divisors of m, Indian J. Pure Appl. Math., 6(11) (1975), 1276-1286.
Martin Klazar, What is an answer? — remarks, results and problems on PIO formulas in combinatorial enumeration, part I, arXiv:1808.08449 [math.CO], 2018.
Noah Lebowitz-Lockard and Joseph Vandehey, On the number of partitions of a number into distinct divisors, arXiv:2402.08119 [math.NT], 2024. See p. 1.
Rémy Sigrist, Colored logarithmic scatterplot of the first 10000 terms (where the color is function of A000005(n)).
Index entries for sequences related to partitions.

Cf. A002577, A027750, A033630, A072721, A161148 (partitions in squared divisors), A171565, A210442, A211110, A225244, A306387, A379957.

Cf. A000005, A001248, A001748, A052147, A100484.

a018818 n = p (init $ a027750_row n) n + 1 where
   p _      0 = 1
   p []     _ = 0
   p ks'@(k:ks) m | m < k     = 0
                  | otherwise = p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Apr 02 2012

[#RestrictedPartitions(n,{d:d in Divisors(n)}): n in [1..100]]; // Marius A. Burtea, Jan 02 2019

A018818 := proc(n)
    local a,p,w,el ;
    a := 0 ;
    for p in combinat[partition](n) do
        w := true ;
        for el in p do
            if modp(n,el) <> 0 then
                w := false;
                break;
            end if;
        end do:
        if w then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Mar 30 2017

Table[d = Divisors[n]; Coefficient[Series[1/Product[1 - x^d[[i]], {i, Length[d]}], {x, 0, n}], x, n], {n, 100}] (* T. D. Noe, Jul 28 2011 *)

a(n)=numbpartUsing(n, divisors(n));
numbpartUsing(n, v, mx=#v)=if(n<1, return(n==0)); sum(i=1,mx, numbpartUsing(n-v[i],v,i)) \\ inefficient; Charles R Greathouse IV, Jun 21 2017

A018818(n) = { my(p = Ser(1, 'x, 1+n)); fordiv(n, d, p /= (1 - 'x^d)); polcoef(p, n); }; \\ Antti Karttunen, Jan 23 2025, after Vladeta Jovovic

Coefficient of x^n in the expansion of 1/Product_{d|n} (1-x^d). - Vladeta Jovovic, Sep 28 2002
a(n) = 2 iff n is prime. - Juhani Heino, Aug 27 2009
a(n) = f(n,n,1), where f(n,m,k) = f(n,m,k+1) + f(n,m-k,k)*0^(n mod k) if k <= m, otherwise 0^m. - Reinhard Zumkeller, Dec 11 2009
Paul Erdős, Andrew M. Odlyzko, and the Editors of the AMM give bounds; see Bowman et al. - Charles R Greathouse IV, Dec 04 2012

A014092 Numbers that are not the sum of 2 primes.

Original entry on oeis.org

1, 2, 3, 11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65, 67, 71, 77, 79, 83, 87, 89, 93, 95, 97, 101, 107, 113, 117, 119, 121, 123, 125, 127, 131, 135, 137, 143, 145, 147, 149, 155, 157, 161, 163, 167, 171, 173, 177, 179, 185, 187, 189, 191, 197, 203, 205, 207, 209

Offset: 1

N. J. A. Sloane

Suggested by the Goldbach conjecture that every even number larger than 2 is the sum of 2 primes.
Since (if we believe the Goldbach conjecture) all the entries > 2 in this sequence are odd, they are equal to 2 + an odd composite number (or 1).
Otherwise said, the sequence consists of 2 and odd numbers k such that k-2 is not prime. In particular there is no element from A006512, greater of a twin prime pair. - M. F. Hasler, Sep 18 2012
Values of k such that A061358(k) = 0. - Emeric Deutsch, Apr 03 2006
Values of k such that A073610(k) = 0. - Graeme McRae, Jul 18 2006

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Section 2.8 (for Goldbach conjecture).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences related to Goldbach conjecture

Cf. A002372, A002373, A002374, A048974, A061358.
Cf. A010051, A000040, A051035 (composites).
Equivalent sequence for prime powers: A071331.
Numbers that can be expressed as the sum of two primes in k ways for k=0..10: this sequence (k=0), A067187 (k=1), A067188 (k=2), A067189 (k=3), A067190 (k=4), A067191 (k=5), A066722 (k=6), A352229 (k=7), A352230 (k=8), A352231 (k=9), A352233 (k=10).

a014092 n = a014092_list !! (n-1)
a014092_list = filter (\x ->
   all ((== 0) . a010051) $ map (x -) $ takeWhile (< x) a000040_list) [1..]
-- Reinhard Zumkeller, Sep 28 2011

g:=sum(sum(x^(ithprime(i)+ithprime(j)),i=1..j),j=1..50): gser:=series(g,x=0,230): a:=proc(n) if coeff(gser,x^n)=0 then n else fi end: seq(a(n),n=1..225); # Emeric Deutsch, Apr 03 2006

s1falsifiziertQ[s_]:= Module[{ip=IntegerPartitions[s, {2}], widerlegt=False},Do[If[PrimeQ[ip[[i,1]] ] ~And~ PrimeQ[ip[[i,2]] ], widerlegt = True; Break[]],{i,1,Length[ip]}];widerlegt]; Select[Range[250],s1falsifiziertQ[ # ]==False&] (* Michael Taktikos, Dec 30 2007 *)
Join[{1,2},Select[Range[3,300,2],!PrimeQ[#-2]&]] (* Zak Seidov, Nov 27 2010 *)
Select[Range[250],Count[IntegerPartitions[#,{2}],?(AllTrue[#,PrimeQ]&)]==0&] (* _Harvey P. Dale, Jun 08 2022 *)

isA014092(n)=local(p,i) ; i=1 ; p=prime(i); while(pA014092(a), print(n," ",a); n++)) \\ R. J. Mathar, Aug 20 2006

from sympy import prime, isprime
def ok(n):
    i=1
    x=prime(i)
    while xIndranil Ghosh, Apr 29 2017

Odd composite numbers + 2 (essentially A014076(n) + 2 ).

Equals {2} union A005408 \ A052147, i.e., essentially the complement of A052147 (or rather A048974) within the odd numbers A005408. - M. F. Hasler, Sep 18 2012

A067187 Numbers that can be expressed as the sum of two primes in exactly one way.

Original entry on oeis.org

4, 5, 6, 7, 8, 9, 12, 13, 15, 19, 21, 25, 31, 33, 39, 43, 45, 49, 55, 61, 63, 69, 73, 75, 81, 85, 91, 99, 103, 105, 109, 111, 115, 129, 133, 139, 141, 151, 153, 159, 165, 169, 175, 181, 183, 193, 195, 199, 201, 213, 225, 229, 231, 235, 241, 243, 253, 259, 265, 271

Offset: 1

Amarnath Murthy, Jan 10 2002

nonn

All primes + 2 are terms of this sequence. Is 12 the last even term? - Frank Ellermann, Jan 17 2002
A048974, A052147, A067187 and A088685 are very similar after dropping terms less than 13. - Eric W. Weisstein, Oct 10 2003
Values of n such that A061358(n)=1. - Emeric Deutsch, Apr 03 2006

			4 is a term as 4 = 2+2, 15 is a term as 15 = 13+2.

Robert Price, Table of n, a(n) for n = 1..5002
Index entries for sequences related to Goldbach conjecture

Cf. A023036, A045917, A061358.
Subsequence of A014091.
Numbers that can be expressed as the sum of two primes in k ways for k=0..10: A014092 (k=0), this sequence (k=1), A067188 (k=2), A067189 (k=3), A067190 (k=4), A067191 (k=5), A066722 (k=6), A352229 (k=7), A352230 (k=8), A352231 (k=9), A352233 (k=10).

g:=sum(sum(x^(ithprime(i)+ithprime(j)),i=1..j),j=1..80): gser:=series(g,x=0,280): a:=proc(n) if coeff(gser,x^n)=1 then n else fi end: seq(a(n),n=1..272); # Emeric Deutsch, Apr 03 2006

cQ[n_]:=Module[{c=0},Do[If[PrimeQ[n-i]&&PrimeQ[i],c++],{i,2,n/2}]; c==1]; Select[Range[4,271],cQ[#]&] (* Jayanta Basu, May 22 2013 *)
y = Select[Flatten@Table[Prime[i] + Prime[j], {i, 60}, {j, 1, i}], # < Prime[60] &]; Select[Union[y], Count[y, #] == 1 &] (* Robert Price, Apr 21 2025 *)

Edited by Frank Ellermann, Jan 17 2002

A113935 a(n) = prime(n) + 3.

Original entry on oeis.org

5, 6, 8, 10, 14, 16, 20, 22, 26, 32, 34, 40, 44, 46, 50, 56, 62, 64, 70, 74, 76, 82, 86, 92, 100, 104, 106, 110, 112, 116, 130, 134, 140, 142, 152, 154, 160, 166, 170, 176, 182, 184, 194, 196, 200, 202, 214, 226, 230, 232, 236, 242, 244, 254, 260, 266, 272, 274

Offset: 1

Jorge Coveiro, Jan 30 2006

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A098090, A116366.

List([1..70], n-> Primes[n]+3); # G. C. Greubel, May 18 2019

[p+3: p in PrimesUpTo(500)]; // Vincenzo Librandi, Nov 27 2013

Prime[Range[70]]+3 (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

PARI
```
for(x=1,100,print1(prime(x)+3,","))
```

[nth_prime(n)+3 for n in (1..70)] # G. C. Greubel, May 18 2019

a(n) = A116366(n-1,1) for n>1. - Reinhard Zumkeller, Feb 06 2006
a(n) = 2*A098090(n-1) for n > 1. - Reinhard Zumkeller, Sep 14 2006
a(n) = A000040(n) + 3 = A008864(n) + 2 = A052147(n) + 1 = A175221(n) - 1 = A175222(n) - 2 = A139049(n) - 3 = A175223(n) - 4 = A175224(n) - 5 = A140353(n) - 6 = A175225(n) - 7. - Jaroslav Krizek, Mar 06 2010

A175222 a(n) = prime(n) + 5.

Original entry on oeis.org

7, 8, 10, 12, 16, 18, 22, 24, 28, 34, 36, 42, 46, 48, 52, 58, 64, 66, 72, 76, 78, 84, 88, 94, 102, 106, 108, 112, 114, 118, 132, 136, 142, 144, 154, 156, 162, 168, 172, 178, 184, 186, 196, 198, 202, 204, 216, 228, 232, 234, 238, 244, 246, 256, 262, 268, 274, 276

Offset: 1

Jaroslav Krizek, Mar 06 2010

a(n) = A000040(n) + 5 = A008864(n) + 4 = A052147(n) + 3 = A113395(n) + 2 = A175221 (n) + 1 = A139049(n) - 1 = A175223(n) - 2 = A175224(n) - 3 = A140353(n) - 4 = A175225(n) - 5.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A008864, A052147, A086801, A113395, A113935, A139049, A140353, A175221, A175223, A175224, A175225.

Filtered([1..300], k-> IsPrime(k) ) + 5; # G. C. Greubel, May 20 2019

[p+5: p in PrimesUpTo(500)]; // Vincenzo Librandi, Dec 04 2010

Prime[Range[120]]+5 (* Vladimir Joseph Stephan Orlovsky, Nov 21 2010 *)

{a(n) = prime(n) + 5}; \\ G. C. Greubel, May 20 2019

[nth_prime(n) + 5 for n in (1..100)] # G. C. Greubel, May 20 2019

More terms from Vincenzo Librandi, Mar 14 2010

A140353 a(n) = prime(n) + 9.

Original entry on oeis.org

11, 12, 14, 16, 20, 22, 26, 28, 32, 38, 40, 46, 50, 52, 56, 62, 68, 70, 76, 80, 82, 88, 92, 98, 106, 110, 112, 116, 118, 122, 136, 140, 146, 148, 158, 160, 166, 172, 176, 182, 188, 190, 200, 202, 206, 208, 220, 232, 236, 238, 242, 248, 250, 260, 266, 272, 278, 280, 286

Offset: 1

Odimar Fabeny, May 30 2008

a(n) = A000040(n) + 9 = A008864(n) + 8 = A052147(n) + 7 = A113395(n) + 6 = A175221(n) + 5 = A175222(n) + 4 = A139049(n) + 3 = A175223(n) + 2 = A175224(n) + 1 = A175225(n) - 1. - Jaroslav Krizek, Mar 06 2010

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A139049

Filtered([1..300], k-> IsPrime(k) ) +9 # G. C. Greubel, May 20 2019

[NthPrime(n)+9: n in [1..70]]; // G. C. Greubel, May 20 2019

9 + Prime[Range[70]] (* G. C. Greubel, May 20 2019 *)

PARI
```
A140353(n) = prime(n)+9
```

[nth_prime(n) +9 for n in (1..70)] # G. C. Greubel, May 20 2019

Edited by Michael B. Porter, Jan 28 2010

A175221 a(n) = prime(n) + 4.

Original entry on oeis.org

6, 7, 9, 11, 15, 17, 21, 23, 27, 33, 35, 41, 45, 47, 51, 57, 63, 65, 71, 75, 77, 83, 87, 93, 101, 105, 107, 111, 113, 117, 131, 135, 141, 143, 153, 155, 161, 167, 171, 177, 183, 185, 195, 197, 201, 203, 215, 227, 231, 233, 237, 243, 245, 255, 261, 267, 273, 275

Offset: 1

Jaroslav Krizek, Mar 06 2010

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Filtered([1..300], k-> IsPrime(k) ) + 4; # G. C. Greubel, May 20 2019

[(p+4):p in PrimesUpTo(500)]; // Vincenzo Librandi, Dec 04 2010

Prime[Range[60]]+4 (* Harvey P. Dale, Jan 01 2013 *)

{a(n) = prime(n) + 4}; \\ G. C. Greubel, May 20 2019

[nth_prime(n) + 4 for n in (1..60)] # G. C. Greubel, May 20 2019

a(n) = A000040(n) + 4 = A008864(n) + 3 = A052147(n) + 2 = A113395(n) + 1.
a(n) = A175222(n) - 1 = A139049(n) - 2 = A175223(n) - 3.
a(n) = A175224(n) - 4 = A140353(n) - 5 = A175225(n) - 6.

More terms from Vincenzo Librandi, Mar 14 2010

A139049 a(n) = prime(n) + 6.

Original entry on oeis.org

8, 9, 11, 13, 17, 19, 23, 25, 29, 35, 37, 43, 47, 49, 53, 59, 65, 67, 73, 77, 79, 85, 89, 95, 103, 107, 109, 113, 115, 119, 133, 137, 143, 145, 155, 157, 163, 169, 173, 179, 185, 187, 197, 199, 203, 205, 217, 229, 233, 235, 239, 245, 247, 257, 263, 269, 275, 277

Offset: 1

Odimar Fabeny, Jun 02 2008

a(n) = A000040(n) + 6 = A008864(n) + 5 = A052147(n) + 4 = A113395(n) + 3 = A175221(n) + 2 = A175222(n) + 1 = A175223(n) - 1 = A175224(n) - 2 = A140353(n) - 3 = A175225(n) - 4. - Jaroslav Krizek, Mar 06 2010

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A140353.

Filtered([1..300], k-> IsPrime(k) ) + 6; # G. C. Greubel, May 20 2019

[NthPrime(n)+6: n in [1..70]]; // G. C. Greubel, May 20 2019

A139049:=n->ithprime(n)+6: seq(A139049(n), n=1..100); # Wesley Ivan Hurt, Apr 18 2017

6+Prime[Range[70]] (* G. C. Greubel, May 20 2019 *)

PARI
```
A139049(n) = prime(n)+6
```

[nth_prime(n) +6 for n in (1..70)] # G. C. Greubel, May 20 2019

Edited by Michael B. Porter, Jan 28 2010

A175223 a(n) = prime(n) + 7.

Original entry on oeis.org

9, 10, 12, 14, 18, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 60, 66, 68, 74, 78, 80, 86, 90, 96, 104, 108, 110, 114, 116, 120, 134, 138, 144, 146, 156, 158, 164, 170, 174, 180, 186, 188, 198, 200, 204, 206, 218, 230, 234, 236, 240, 246, 248, 258, 264, 270, 276, 278

Offset: 1

Jaroslav Krizek, Mar 06 2010

a(n) = A000040(n) + 7 = A008864(n) + 6 = A052147(n) + 5 = A113395(n) + 4 = A175221(n) + 3 = A175222 (n) + 2 = A139049(n) + 1 = A175224(n) - 1 = A140353(n) - 2 = A175225(n) - 3.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Filtered([1..300], k-> IsPrime(k) ) + 7; # G. C. Greubel, May 20 2019

[p+7: p in PrimesUpTo(500)]; // Vincenzo Librandi, Dec 04 2010

Prime[Range[70]] + 7 (* Vincenzo Librandi, Nov 27 2013 *)

{a(n) = prime(n) + 7}; \\ G. C. Greubel, May 20 2019

[nth_prime(n) + 7 for n in (1..70)] # G. C. Greubel, May 20 2019

More terms from Vincenzo Librandi, Mar 14 2010

cp's OEIS Frontend

A008472 Sum of the distinct primes dividing n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Magma

Maple

Mathematica

PARI

PARI

PARI

Python

Sage

Sage

Formula

A018818 Number of partitions of n into divisors of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Magma

Maple

Mathematica

PARI

PARI

Formula

A014092 Numbers that are not the sum of 2 primes.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Python

Formula

A067187 Numbers that can be expressed as the sum of two primes in exactly one way.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A113935 a(n) = prime(n) + 3.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Mathematica

PARI

Sage

Formula

A175222 a(n) = prime(n) + 5.

Views

Author