A353019 Heptagonal numbers which are products of five distinct primes.

32890, 48790, 102718, 167314, 236698, 239785, 260338, 330694, 360430, 389470, 455182, 749938, 884170, 932386, 960070, 1007110, 1104565, 1334806, 1397638, 1423930, 1488802, 1515934, 1610818, 1679770, 1721005, 1741810, 1952314, 2046205, 2312167, 2365363, 2473570, 2503501, 2513518, 2558842

Offset: 1

Author

Massimo Kofler, Apr 17 2022

Keywords

• nonn

Comments

A squarefree subsequence of heptagonal numbers.

Examples

			32890 = 2*5*11*13*23 = 115(5*115-3)/2.
48790 = 2*5*7*17*41 = 140(5*140-3)/2.
102718 = 2*7*11*23*29 = 203(5*203-3)/2.
167314 = 2*7*17*19*37 = 259(5*259-3)/2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000566 and A046387.

Programs

Maple

f:= proc(n) local k, F;
  k:= n*(5*n-3)/2;
  F:= ifactors(k)[2];
  if F[..,2] = [1,1,1,1,1] then k fi
end proc:
map(f, [$1..2000]); # Robert Israel, Jul 29 2025

Mathematica

Select[Table[n*(5*n - 3)/2, {n, 1, 1000}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1} &] (* Amiram Eldar, Apr 17 2022 *)

Python

from sympy import factorint
from itertools import count, islice
def agen():
    for h in (n*(5*n-3)//2 for n in count(1)):
        f = factorint(h, multiple=True)
        if len(f) == len(set(f)) == 5: yield h
print(list(islice(agen(), 34))) # Michael S. Branicky, May 28 2022