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.
%I A088318 #11 Jun 18 2025 07:33:38
%S A088318 0,0,0,0,1,1,2,3,5,7,10,13,18,24,32,40,51,66,83,103,128,158,194,237,
%T A088318 288,348,419,500,601,718,846,1003,1186,1392,1638,1915,2232,2605,3027,
%U A088318 3518,4066,4704,5419,6241,7178,8236,9427,10792,12308,14062,15990,18203,20659
%N A088318 The number of possible values of the squarefree kernel (A007947) shared by at least two solutions x to A056239(x) = n.
%C A088318 Previous name: Number of different values of A007947(m_k) when A007947(m_j) = A007947(m_k) and A056239(m_j) = A056239(m_k) = n, where k>1 ( j runs from 1 to k-1 ).
%C A088318 Without the restriction of being shared by at least two solutions, the number of possible values of the squarefree kernel of the solutions x to A056239(x) = n is A088314(n). - _Amiram Eldar_, Jun 18 2025
%H A088318 Amiram Eldar, <a href="/A088318/b088318.txt">Table of n, a(n) for n = 1..99</a>
%e A088318 a(7) = 2 because there are two different values, 10 and 6:
%e A088318 m_1 = 50, m_2 = 80, 10 = A007947(50) = A007947(80) and A056239(50) = A056239(80) = 7.
%e A088318 m_1 = 54, m_2 = 72, m_3 = 96, 6 = A007947(54) = A007947(72) = A007947(96) and A056239(54) = A056239(72) = A056239(96) = 7.
%t A088318 a[n_] := Count[Tally[DeleteDuplicates /@ IntegerPartitions[n]][[;; , 2]], _?(# > 1 &)]; Array[a, 50] (* _Amiram Eldar_, Jun 18 2025 *)
%o A088318 (PARI) a(n) = {my(v = List(), c = 0); forpart(p = n, listput(v, vecprod(apply(prime, Set(p))))); v = matreduce(Vec(v))[,2]; for(i = 1, #v, if(v[i] > 1, c++)); c;} \\ _Amiram Eldar_, Jun 18 2025
%Y A088318 Cf. A007947, A056239, A088314, A088850.
%K A088318 nonn
%O A088318 1,7
%A A088318 _Naohiro Nomoto_, Nov 06 2003
%E A088318 Name changed, a(29) corrected and (30)-a(53) added by _Amiram Eldar_, Jun 18 2025