cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A056675 Number of non-unitary but squarefree divisors of n!. Also number of unitary but not-squarefree divisors of n!.

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%I A056675 #18 May 02 2022 22:02:46
%S A056675 0,0,0,2,4,6,12,12,12,14,28,28,56,60,60,60,120,120,240,240,240,248,
%T A056675 496,496,496,504,504,504,1008,1008,2016,2016,2016,2032,2032,2032,4064,
%U A056675 4080,4080,4080,8160,8160,16320,16320,16320,16352,32704,32704,32704,32704
%N A056675 Number of non-unitary but squarefree divisors of n!. Also number of unitary but not-squarefree divisors of n!.
%H A056675 Amiram Eldar, <a href="/A056675/b056675.txt">Table of n, a(n) for n = 1..10000</a>
%F A056675 a(n) = A048656(n) - A000005(A055231(n!)) = A048656(n) - A000005(A007913(n!)/A055229(n!)).
%F A056675 a(n) = A056674(A000142(n)). - _Amiram Eldar_, Aug 06 2019
%F A056675 a(n) = A048656(n) - A056672(n). - _Sean A. Irvine_, May 02 2022
%e A056675 n=10: 10! = 2*2*2*2*2*2*2*2*3*3*3*3*5*5*7 = 256*81*25*7, which has 270 divisors, of which 16 are unitary and 16 are squarefree; overlap={1,7}. The set {2, 3, 5, 6, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210} represents the squarefree non-unitary divisors of 10!, so a(10)=14.
%o A056675 (PARI) a(n) = my(f=n!); sumdiv(f, d, issquarefree(d) && (gcd(d, f/d) != 1)); \\ _Michel Marcus_, Sep 05 2017
%Y A056675 Cf. A000005, A000142, A007913, A048656, A055229, A055231, A056674, A056772.
%K A056675 nonn
%O A056675 1,4
%A A056675 _Labos Elemer_, Aug 10 2000