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A368426 Centered 10-gonal numbers which are sphenic numbers.

%I A368426 #17 Jan 25 2024 02:40:44
%S A368426 20801,22781,37411,47531,55651,75031,80011,100111,120901,133661,
%T A368426 161101,177661,191101,199001,201001,230051,236531,240901,245311,
%U A368426 263351,279661,289201,313751,323851,326401,368561,376751,436601,439561,445511,472781,475861,488281,507211,539561
%N A368426 Centered 10-gonal numbers which are sphenic numbers.
%H A368426 Robert Israel, <a href="/A368426/b368426.txt">Table of n, a(n) for n = 1..5080</a>
%e A368426 A062786(65) = 20801 = 5 * 65 * (65-1) + 1 = 11 * 31 * 61.
%e A368426 A062786(68) = 22781 = 5 * 68 * (68-1) + 1 = 11 * 19 * 109.
%p A368426 isc10:= proc(n) issqr(20*n+5) end proc:
%p A368426 P:= select(isprime, [seq(seq(10*i+j,j=[-1,1]),i=1..1000)]): nP:= nops(P):
%p A368426 M:= P[1]*P[2]*P[-1]:
%p A368426 A:= NULL:
%p A368426 for i from 1 to nP-2 while P[i]^3 < M do
%p A368426   for j from i+1 to nP-1 while P[i]*P[j]^2 < M do
%p A368426     for k from j+1 to nP do
%p A368426       q:= P[i]*P[j]*P[k];
%p A368426       if q > M then break fi;
%p A368426       if isc10(q) then A:= A,q fi
%p A368426 od od od:
%p A368426 sort([A]); # _Robert Israel_, Dec 24 2023
%t A368426 Select[Table[5*n*(n+1) + 1, {n, 1, 330}], FactorInteger[#][[;; , 2]] == {1, 1, 1} &] (* _Amiram Eldar_, Dec 24 2023 *)
%Y A368426 Intersection of A007304 and A062786.
%K A368426 nonn
%O A368426 1,1
%A A368426 _Massimo Kofler_, Dec 24 2023