A048803 -id:A048803 - cp's OEIS frontend

A352372 Triangle read by rows. Let R(n, k) = Y(n, k, B) where Y are the partial Bell polynomials and B is the list [Bernoulli(j, 1), j = 0..n]. T(n, k) are R(n, k) normalized by the lcm of the denominators of the terms in row n (A048803).

1, 0, 1, 0, 1, 2, 0, 1, 9, 6, 0, 0, 17, 36, 12, 0, -2, 50, 325, 300, 60, 0, 0, 28, 2475, 5250, 2700, 360, 0, 60, -882, 14161, 77175, 80850, 26460, 2520, 0, 0, -608, 5488, 239267, 499800, 311640, 70560, 5040, 0, -504, 6480, -57404, 735588, 3563721, 3969000, 1640520, 272160, 15120

Offset: 0

Peter Luschny, Mar 14 2022

			Triangle starts:
[0] 1;
[1] 0,    1;
[2] 0,    1,     2;
[3] 0,    1,     9,      6;
[4] 0,    0,    17,     36,      12;
[5] 0,   -2,    50,    325,     300,      60;
[6] 0,    0,    28,   2475,    5250,    2700,     360;
[7] 0,   60,  -882,  14161,   77175,   80850,   26460,   2520;
[8] 0,    0,  -608,   5488,  239267,  499800,  311640,  70560,  5040;
.
For example row 7 is 2520*[R(7, k), k = 0..7] = 2520*[0, 1/42, -7/20, 2023/360, 245/8, 385/12, 21/2, 1] since lcm(1, 42, 20, 360, 8, 12, 2, 1) = A048803(7) = 2520. Conversely, since R(n, n) = 1 and T(n, n) = Product_{k=1..n} rad(k), the R(n, k) can be obtained by dividing the terms of row n by T(n, n).

Cf. A027641/A027642, A048803, A007947, A264428 (Bell transform).

B[n_, k_] := BellY[n, k, Table[BernoulliB[j, 1], {j, 0, n}]];
P[n_] := Select[Divisors[n], PrimeQ];
T[n_, k_] := B[n, k] Product[Product[p, {p, P[j]}], {j, 1, n}];
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten

T(n, n) = Product_{k=1..n} rad(k) = Product_{k=1..n} A007947(k) = A048803(n).

A007947 Largest squarefree number dividing n: the squarefree kernel of n, rad(n), radical of n.

Original entry on oeis.org

1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, 21, 22, 23, 6, 5, 26, 3, 14, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 10, 41, 42, 43, 22, 15, 46, 47, 6, 7, 10, 51, 26, 53, 6, 55, 14, 57, 58, 59, 30, 61, 62, 21, 2, 65, 66, 67, 34, 69, 70, 71, 6, 73, 74, 15, 38, 77, 78

Offset: 1

R. Muller, Mar 15 1996

Multiplicative with a(p^e) = p.
Product of the distinct prime factors of n.
a(k)=k for k=squarefree numbers A005117. - Lekraj Beedassy, Sep 05 2006
A note on square roots of numbers: we can write sqrt(n) = b*sqrt(c) where c is squarefree. Then b = A000188(n) is the "inner square root" of n, c = A007913(n), b*c = A019554(n) = "outer square root" of n, and a(n) = lcm(a(b),c). Unless n is biquadrateful (A046101), a(n) = lcm(b,c). [Edited by Jeppe Stig Nielsen, Oct 10 2021, and Andrey Zabolotskiy, Feb 12 2025]
a(n) = A128651(A129132(n-1) + 2) for n > 1. - Reinhard Zumkeller, Mar 30 2007
Also the least common multiple of the prime factors of n. - Peter Luschny, Mar 22 2011
The Mobius transform of the sequence generates the sequence of absolute values of A097945. - R. J. Mathar, Apr 04 2011
Appears to be the period length of k^n mod n. For example, n^12 mod 12 has period 6, repeating 1,4,9,4,1,0, so a(12)= 6. - Gary Detlefs, Apr 14 2013
a(n) differs from A014963(n) when n is a term of A024619. - Eric Desbiaux, Mar 24 2014
a(n) is also the smallest base (also termed radix) for which the representation of 1/n is of finite length.  For example a(12) = 6 and 1/12 in base 6 is 0.03, which is of finite length. - Lee A. Newberg, Jul 27 2016
a(n) is also the divisor k of n such that d(k) = 2^omega(n). a(n) is also the smallest divisor u of n such that n divides u^n. - Juri-Stepan Gerasimov, Apr 06 2017

			G.f. = x + 2*x^2 + 3*x^3 + 2*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 2*x^8 + 3*x^9 + ... - _Michael Somos_, Jul 15 2018

Daniel Forgues, Table of n, a(n) for n = 1..100000 (first 10000 terms from T. D. Noe)
Masum Billal, Divisible Sequence and its Characteristic Sequence, arXiv:1501.00609 [math.NT], 2015, theorem 11 page 5.
Henry Bottomley, Some Smarandache-type multiplicative sequences
Steven R. Finch, Unitarism and Infinitarism, February 25, 2004. [Cached copy, with permission of the author]
Jarosław Grytczuk, Thue type problems for graphs, points and numbers, Discrete Math., 308 (2008), 4419-4429.
Neville Holmes, Integer Sequences [Broken link]
Serge Lang, Old and New Conjectured Diophantine Inequalities, Bull. Amer. Math. Soc., 23 (1990), 37-75. see p. 39.
Wolfdieter Lang, Cantor's List of Real Algebraic Numbers of Heights 1 to 7, arXiv:2307.10645 [math.NT], 2023.
D. H. Lehmer, Euler constants for arithmetical progressions, Collection of articles in memory of Juriĭ Vladimirovič Linnik. Acta Arith. 27 (1975), 125--142. MR0369233 (51 #5468). See N_k on page 131.
Ivar Peterson, The Amazing ABC Conjecture
Paul Tarau, Emulating Primality with Multiset Representations of Natural Numbers, in Theoretical Aspects of Computing, ICTAC 2011, Lecture Notes in Computer Science, 2011, Volume 6916/2011, 218-238
Paul Tarau, Towards a generic view of primality through multiset decompositions of natural numbers, Theoretical Computer Science, Volume 537, 5 June 2014, Pages 105-124.
Wikipedia, Radical of an integer.

See A007913, A062953, A000188, A019554, A003557, A066503, A087207 for other properties related to square and squarefree divisors of n.
More general factorization-related properties, specific to n: A020639, A028234, A020500, A010051, A284318, A000005, A001221, A005361, A034444, A014963, A128651, A267116.
Range of values is A005117.
Cf. A048803, A019565, A024619, A053462, A060735, A073355 (partial sums), A079277, A097945, A129132, A225546.
Bisections: A099984, A099985.
Sequences about numbers that have the same squarefree kernel: A065642, array A284311 (A284457).
A003961, A059896 are used to express relationship between terms of this sequence.
Cf. A001615, A008683, A076479, A078615.

a007947 = product . a027748_row  -- Reinhard Zumkeller, Feb 27 2012

[ &*PrimeDivisors(n): n in [1..100] ]; // Klaus Brockhaus, Dec 04 2008

with(numtheory); A007947 := proc(n) local i,t1,t2; t1 := ifactors(n)[2]; t2 := mul(t1[i][1],i=1..nops(t1)); end;
A007947 := n -> ilcm(op(numtheory[factorset](n))):
seq(A007947(i),i=1..69); # Peter Luschny, Mar 22 2011
A:= n -> convert(numtheory:-factorset(n),`*`):
seq(A(n),n=1..100); # Robert Israel, Aug 10 2014
seq(NumberTheory:-Radical(n), n = 1..78); # Peter Luschny, Jul 20 2021

rad[n_] := Times @@ (First@# & /@ FactorInteger@ n); Array[rad, 78] (* Robert G. Wilson v, Aug 29 2012 *)
Table[Last[Select[Divisors[n],SquareFreeQ]],{n,100}] (* Harvey P. Dale, Jul 14 2014 *)
a[ n_] := If[ n < 1, 0, Sum[ EulerPhi[d] Abs @ MoebiusMu[d], {d, Divisors[ n]}]]; (* Michael Somos, Jul 15 2018 *)
Table[Product[p, {p, Select[Divisors[n], PrimeQ]}], {n, 1, 100}] (* Vaclav Kotesovec, May 20 2020 *)

a(n) = factorback(factorint(n)[,1]); \\ Andrew Lelechenko, May 09 2014

for(n=1, 100, print1(direuler(p=2, n, (1 + p*X - X)/(1 - X))[n], ", ")) \\ Vaclav Kotesovec, Jun 14 2020

from sympy import primefactors, prod
def a(n): return 1 if n < 2 else prod(primefactors(n))
[a(n) for n in range(1, 51)]  # Indranil Ghosh, Apr 16 2017

def A007947(n): return mul(p for p in prime_divisors(n))
[A007947(n) for n in (1..60)] # Peter Luschny, Mar 07 2017

(define (A007947 n) (if (= 1 n) n (* (A020639 n) (A007947 (A028234 n))))) ;; ;; Needs also code from A020639 and A028234. - Antti Karttunen, Jun 18 2017

If n = Product_j (p_j^k_j) where p_j are distinct primes, then a(n) = Product_j (p_j).
a(n) = Product_{k=1..A001221(n)} A027748(n,k). - Reinhard Zumkeller, Aug 27 2011
Dirichlet g.f.: zeta(s)*Product_{primes p} (1+p^(1-s)-p^(-s)). - R. J. Mathar, Jan 21 2012
a(n) = Sum_{d|n} phi(d) * mu(d)^2 = Sum_{d|n} |A097945(d)|. - Enrique Pérez Herrero, Apr 23 2012
a(n) = Product_{d|n} d^moebius(n/d) (see Billal link). - Michel Marcus, Jan 06 2015
a(n) = n/( Sum_{k=1..n} (floor(k^n/n)-floor((k^n - 1)/n)) ) = e^(Sum_{k=2..n} (floor(n/k) - floor((n-1)/k))*A010051(k)*M(k)) where M(n) is the Mangoldt function. - Anthony Browne, Jun 17 2016
a(n) = n/A003557(n). - Juri-Stepan Gerasimov, Apr 07 2017
G.f.: Sum_{k>=1} phi(k)*mu(k)^2*x^k/(1 - x^k). - Ilya Gutkovskiy, Apr 11 2017
From Antti Karttunen, Jun 18 2017: (Start)
a(1) = 1; for n > 1, a(n) = A020639(n) * a(A028234(n)).
a(n) = A019565(A087207(n)). (End)
Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{primes p} (1 + p^(1-2*s) - p^(2-2*s) - p^(-s)). - Vaclav Kotesovec, Dec 18 2019
From Peter Munn, Jan 01 2020: (Start)
a(A059896(n,k)) = A059896(a(n), a(k)).
a(A003961(n)) = A003961(a(n)).
a(n^2) = a(n).
a(A225546(n)) = A019565(A267116(n)). (End)
Sum_{k=1..n} a(k) ~ c * n^2, where c = A065463/2. - Vaclav Kotesovec, Jun 24 2020
From Richard L. Ollerton, May 07 2021: (Start)
a(n) = Sum_{k=1..n} mu(n/gcd(n,k))^2.
a(n) = Sum_{k=1..n} mu(gcd(n,k))^2*phi(gcd(n,k))/phi(n/gcd(n,k)).
For n>1, Sum_{k=1..n} a(gcd(n,k))*mu(a(gcd(n,k)))*phi(gcd(n,k))/gcd(n,k) = 0.
For n>1, Sum_{k=1..n} a(n/gcd(n,k))*mu(a(n/gcd(n,k)))*phi(gcd(n,k))*gcd(n,k) = 0. (End)
a(n) = (-1)^omega(n) * Sum_{d|n} mu(d)*psi(d), where omega = A001221 and psi = A001615. - Ridouane Oudra, Aug 01 2025

More terms from several people including David W. Wilson

Definition expanded by Jonathan Sondow, Apr 26 2013

A013939 Partial sums of sequence A001221 (number of distinct primes dividing n).

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 15, 17, 19, 20, 21, 23, 24, 26, 28, 30, 31, 33, 34, 36, 37, 39, 40, 43, 44, 45, 47, 49, 51, 53, 54, 56, 58, 60, 61, 64, 65, 67, 69, 71, 72, 74, 75, 77, 79, 81, 82, 84, 86, 88, 90, 92, 93, 96, 97, 99, 101, 102, 104, 107, 108, 110, 112

Offset: 1

N. J. A. Sloane, Henri Lifchitz

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Distinct Prime Factors

Cf. A005187, A006218, A011371, A013936.
Cf. A093614, A048865, A006218.
Cf. A027748, A000040, A082287.
Cf. A022559.
Cf. A077761.
Cf. A346617.
Cf. A001222, A048803.

a013939 n = a013939_list !! (n-1)
a013939_list = scanl1 (+) $ map a001221 [1..]
-- Reinhard Zumkeller, Feb 16 2012

[(&+[Floor(n/NthPrime(k)): k in [1..n]]): n in [1..70]]; // G. C. Greubel, Nov 24 2018

A013939 := proc(n) option remember;  `if`(n = 1, 0, a(n) + iquo(n+1, ithprime(n+1))) end:
seq(A013939(i), i = 1..69);  # Peter Luschny, Jul 16 2011

a[n_] := Sum[Floor[n/Prime[k]], {k, 1, n}]; Table[a[n], {n, 1, 69}] (* Jean-François Alcover, Jun 11 2012, from 2nd formula *)
Accumulate[PrimeNu[Range[120]]] (* Harvey P. Dale, Jun 05 2015 *)

t=0;vector(99,n,t+=omega(n)) \\ Charles R Greathouse IV, Jan 11 2012

a(n)=my(s);forprime(p=2,n,s+=n\p);s \\ Charles R Greathouse IV, Jan 11 2012

a(n) = sum(k=1, sqrtint(n), k * (primepi(n\k) - primepi(n\(k+1)))) + sum(k=1, n\(sqrtint(n)+1), if(isprime(k), n\k, 0)); \\ Daniel Suteu, Nov 24 2018

from sympy.ntheory import primefactors
print([sum(len(primefactors(k)) for k in range(1,n+1)) for n in range(1, 121)]) # Indranil Ghosh, Mar 19 2017

from sympy import primerange
def A013939(n): return sum(n//p for p in primerange(n+1)) # Chai Wah Wu, Oct 06 2024

[sum(floor(n/nth_prime(k)) for k in (1..n)) for n in (1..70)] # G. C. Greubel, Nov 24 2018

a(n) = Sum_{k <= n} omega(k).
a(n) = Sum_{k = 1..n} floor( n/prime(k) ).
a(n) = a(n-1) + A001221(n).
a(n) = A093614(n) - A048865(n); see also A006218.
A027748(a(A000040(n))+1) = A000040(n), A082287(a(n)+1) = n.
a(n) = Sum_{k=1..n} pi(floor(n/k)). - Vladeta Jovovic, Jun 18 2006
a(n) = n log log n + O(n). - Charles R Greathouse IV, Jan 11 2012
a(n) = n*(log log n + B) + o(n), where B = 0.261497... is the Mertens constant A077761. - Arkadiusz Wesolowski, Oct 18 2013
G.f.: (1/(1 - x))*Sum_{k>=1} x^prime(k)/(1 - x^prime(k)). - Ilya Gutkovskiy, Jan 02 2017
a(n) = Sum_{k=1..floor(sqrt(n))} k * (pi(floor(n/k)) - pi(floor(n/(k+1)))) + Sum_{p prime <= floor(n/(1+floor(sqrt(n))))} floor(n/p). - Daniel Suteu, Nov 24 2018
a(n) = Sum_{k>=1} k * A346617(n,k). - Alois P. Heinz, Aug 19 2021
a(n) = A001222(A048803(n+1)). - Flávio V. Fernandes, Jan 14 2025

More terms from Henry Bottomley, Jul 03 2001

A060238 a(n) = det(M) where M is an n X n matrix with M[i,j] = lcm(i,j).

Original entry on oeis.org

1, 1, -2, 12, -48, 960, 11520, -483840, 3870720, -69672960, -2786918400, 306561024000, 7357464576000, -1147764473856000, -96412215803904000, -11569465896468480000, 185111454343495680000, -50350315581430824960000, -1812611360931509698560000

Offset: 0

MCKAY john (mckay(AT)cs.concordia.ca), Mar 21 2001

sign

J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 695, pp. 90, 297-298, Ellipses, Paris, 2004.
J. Sandor and B. Crstici, Handbook of Number Theory II, Springer, 2004, p. 265, eq. 10.

Enrique Pérez Herrero, Table of n, a(n) for n = 0..200
Index to sequences related to determinants.

Cf. A000142, A001088, A013939, A023900, A048803, A060239, A085542.

A060238:=n->n!*mul((1-ithprime(i))^floor(n/ithprime(i)), i=1..numtheory[pi](n)): seq(A060238(n), n=0..20); # Wesley Ivan Hurt, Aug 15 2016

A060238[n_]:=n!*Product[(1 - Prime[i])^Floor[n/Prime[i]], {i, PrimePi[n]}]; Array[A060238, 20] (* Enrique Pérez Herrero, Jun 08 2010 *)

a(n)=n!*prod(p=1,sqrtint(n),if(isprime(p),(1-p)^floor(n/p),1)) \\ Benoit Cloitre, Jan 31 2008

For n >= 2, a(n) = n! * Product_{j=2..n} Product_{p|j} (1-p) (where the second product is over all primes p that divide j) (cf. A023900). - Avi Peretz (njk(AT)netvision.net.il), Mar 22 2001
a(n) = n! * Product_{p<=n} (1-p)^floor(n/p) where the product runs through the primes. - Benoit Cloitre, Jan 31 2008
a(n) = A000142(n) * A085542(n). - Enrique Pérez Herrero, Jun 08 2010
a(n) = A001088(n) * A048803(n) * (-1)^A013939(n). - Amiram Eldar, Dec 19 2018
a(n) = Product_{k=1..n} (-1)^A001221(k) * A000010(k) * A007947(k) [De Koninck & Mercier]. - Bernard Schott, Dec 11 2020

a(0)=1 prepended by Alois P. Heinz, Jan 25 2023

A277174 a(n) = Product_{i=1..n} i*rad(i) where rad(n) = A007947(n).

Original entry on oeis.org

1, 1, 4, 36, 288, 7200, 259200, 12700800, 203212800, 5486745600, 548674560000, 66389621760000, 4780052766720000, 807828917575680000, 158334467844833280000, 35625255265087488000000, 1140008168482799616000000, 329462360691529089024000000

Offset: 0

Peter Luschny, Oct 02 2016

nonn

Robert Israel, Table of n, a(n) for n = 0..268

Cf. A007947, A048803.

A277174 := proc(n) local rad, i;
rad := n -> mul(k, k in numtheory:-factorset(n));
mul(i * rad(i), i=1..n) end:
seq(A277174(i), i=0..17);

Table[Product[i Last@ Select[Divisors@ i, SquareFreeQ], {i, n}], {n, 0, 17}] (* Michael De Vlieger, Oct 02 2016 *)

a(n) = prod(i=1, n, i*factorback(factorint(i)[, 1])); \\ Michel Marcus, Oct 03 2016

a(n) = n! * A048803(n). - Robert Israel, Oct 02 2016

A368048 a(n) = lcm_{p in Partitions(n)} (Product_{t in p}(t + m)), where m = 2.

Original entry on oeis.org

1, 3, 36, 540, 6480, 136080, 8164800, 24494400, 293932800, 48498912000, 4073908608000, 158882435712000, 9532946142720000, 28598838428160000, 343186061137920000, 612587119131187200000, 7351045429574246400000, 419009589485732044800000, 276546329060583149568000000

Offset: 0

Peter Luschny, Dec 12 2023

nonn

With m = 0, the cumulative radical A048803 is computed, and with m = 1 the Hirzebruch numbers A091137. The general array is A368116. Using the terminology introduced in A368116 a(n) = lcm_{p in P_{2}(n)} Prod(p).

			Let n = 4. The partitions of 4 are [(4), (3, 1), (2, 2), (2, 1, 1), (1, 1, 1, 1)]. Thus a(4) = lcm([6, 5*3, 4*4, 4*3*3, 3*3*3*3]) = 6480.

Cf. A368092, A048803, A091137, A368116.

def a(n): return lcm(product(r + 2 for r in p) for p in Partitions(n))
print([a(n) for n in range(20)])

a(n) = A368092(n) * 2^(n - n mod 2).

A368116 A(m, n) = lcm_{p in Partitions(n)} (Product_{r in p}(r + m)). Array read by ascending antidiagonals, for m, n >= 0.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 3, 12, 6, 1, 4, 36, 24, 12, 1, 5, 80, 540, 720, 60, 1, 6, 150, 960, 6480, 1440, 360, 1, 7, 252, 5250, 134400, 136080, 60480, 2520, 1, 8, 392, 1512, 315000, 537600, 8164800, 120960, 5040, 1, 9, 576, 24696, 63504, 1575000, 32256000, 24494400, 3628800, 15120

Offset: 0

Peter Luschny, Dec 12 2023

We say q is a 'm-shifted partition of n' if there is a partition p of n, p = (t1, t2, ..., tk) and q = (t1 + m, t2 + m, ..., tk + m), where m is a nonnegative integer. q is a partition of n + k*m.
Let P(n) denote the partitions of n and P_{m}(n) the m-shifted partitions of n. The product of a partition is the product of its parts, Prod(p) = p1*p2*...*pk if p = (p1, p2, ..., pk). Using this terminology, the definition can be written as A(m, n) = lcm_{p in P_{m}(n)} Prod(p).
With m = 0 the cumulative radical A048803 is computed, and with m = 1 the Hirzebruch numbers A091137.

			Array A(m, n) begins:
  [0] 1, 1,   2,     6,       12,        60,           360, ...  A048803
  [1] 1, 2,  12,    24,      720,      1440,         60480, ...  A091137
  [2] 1, 3,  36,   540,     6480,    136080,       8164800, ...  A368048
  [3] 1, 4,  80,   960,   134400,    537600,      32256000, ...
  [4] 1, 5, 150,  5250,   315000,   1575000,     330750000, ...
  [5] 1, 6, 252,  1512,    63504,   1905120,     880165440, ...
  [6] 1, 7, 392, 24696,  6914880, 532445760,  268352663040, ...
  [7] 1, 8, 576, 23040, 18247680, 145981440,  683193139200, ...
  [8] 1, 9, 810, 80190,  7217100, 844400700, 5851696851000, ...
.
Let m = 2 and n = 4. The partitions of 4 are [(4), (3,1), (2,2), (2,1,1), (1, 1, 1, 1)]. Thus A(2, 4) = lcm([6, 5*3, 4*4, 4*3*3, 3*3*3*3]) = 6480.

Cf. A048803 (m=0), A091137 (m=1), A368048 (m=2).

Columns include: A000027, A011379.

def A(m, n): return lcm(product(r + m for r in p) for p in Partitions(n))
for m in range(9): print([A(m, n) for n in range(7)])

cp's OEIS Frontend

A048804 Triangle: T(n,k)=b(n)/(b(k)*b(n-k)) where b is A048803.

Views

Author

Keywords

Examples

Links

Programs

Maple

A352372 Triangle read by rows. Let R(n, k) = Y(n, k, B) where Y are the partial Bell polynomials and B is the list [Bernoulli(j, 1), j = 0..n]. T(n, k) are R(n, k) normalized by the lcm of the denominators of the terms in row n (A048803).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

A007947 Largest squarefree number dividing n: the squarefree kernel of n, rad(n), radical of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Magma

Maple

Mathematica

PARI

PARI

Python

Sage

Scheme

Formula

Extensions

A013939 Partial sums of sequence A001221 (number of distinct primes dividing n).

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Magma

Maple

Mathematica

PARI

PARI

PARI

Python

Python

Sage

Formula

Extensions

A060238 a(n) = det(M) where M is an n X n matrix with M[i,j] = lcm(i,j).

Views

Author

Keywords

References

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions

A277174 a(n) = Product_{i=1..n} i*rad(i) where rad(n) = A007947(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI