A368426 Centered 10-gonal numbers which are sphenic numbers.

20801, 22781, 37411, 47531, 55651, 75031, 80011, 100111, 120901, 133661, 161101, 177661, 191101, 199001, 201001, 230051, 236531, 240901, 245311, 263351, 279661, 289201, 313751, 323851, 326401, 368561, 376751, 436601, 439561, 445511, 472781, 475861, 488281, 507211, 539561

Offset: 1

Author

Massimo Kofler, Dec 24 2023

Keywords

• nonn

Examples

			A062786(65) = 20801 = 5 * 65 * (65-1) + 1 = 11 * 31 * 61.
A062786(68) = 22781 = 5 * 68 * (68-1) + 1 = 11 * 19 * 109.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..5080

Crossrefs

Intersection of A007304 and A062786.

Programs

Maple

isc10:= proc(n) issqr(20*n+5) end proc:
P:= select(isprime, [seq(seq(10*i+j,j=[-1,1]),i=1..1000)]): nP:= nops(P):
M:= P[1]*P[2]*P[-1]:
A:= NULL:
for i from 1 to nP-2 while P[i]^3 < M do
  for j from i+1 to nP-1 while P[i]*P[j]^2 < M do
    for k from j+1 to nP do
      q:= P[i]*P[j]*P[k];
      if q > M then break fi;
      if isc10(q) then A:= A,q fi
od od od:
sort([A]); # Robert Israel, Dec 24 2023

Mathematica

Select[Table[5*n*(n+1) + 1, {n, 1, 330}], FactorInteger[#][[;; , 2]] == {1, 1, 1} &] (* Amiram Eldar, Dec 24 2023 *)