cp's OEIS Frontend

A353019 Heptagonal numbers which are products of five distinct primes.

%I A353019 #39 Jul 29 2025 19:08:04
%S A353019 32890,48790,102718,167314,236698,239785,260338,330694,360430,389470,
%T A353019 455182,749938,884170,932386,960070,1007110,1104565,1334806,1397638,
%U A353019 1423930,1488802,1515934,1610818,1679770,1721005,1741810,1952314,2046205,2312167,2365363,2473570,2503501,2513518,2558842
%N A353019 Heptagonal numbers which are products of five distinct primes.
%C A353019 A squarefree subsequence of heptagonal numbers.
%H A353019 Robert Israel, <a href="/A353019/b353019.txt">Table of n, a(n) for n = 1..10000</a>
%e A353019 32890 = 2*5*11*13*23 = 115(5*115-3)/2.
%e A353019 48790 = 2*5*7*17*41 = 140(5*140-3)/2.
%e A353019 102718 = 2*7*11*23*29 = 203(5*203-3)/2.
%e A353019 167314 = 2*7*17*19*37 = 259(5*259-3)/2.
%p A353019 f:= proc(n) local k, F;
%p A353019   k:= n*(5*n-3)/2;
%p A353019   F:= ifactors(k)[2];
%p A353019   if F[..,2] = [1,1,1,1,1] then k fi
%p A353019 end proc:
%p A353019 map(f, [$1..2000]); # _Robert Israel_, Jul 29 2025
%t A353019 Select[Table[n*(5*n - 3)/2, {n, 1, 1000}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1} &] (* _Amiram Eldar_, Apr 17 2022 *)
%o A353019 (Python)
%o A353019 from sympy import factorint
%o A353019 from itertools import count, islice
%o A353019 def agen():
%o A353019     for h in (n*(5*n-3)//2 for n in count(1)):
%o A353019         f = factorint(h, multiple=True)
%o A353019         if len(f) == len(set(f)) == 5: yield h
%o A353019 print(list(islice(agen(), 34))) # _Michael S. Branicky_, May 28 2022
%Y A353019 Intersection of A000566 and A046387.
%K A353019 nonn
%O A353019 1,1
%A A353019 _Massimo Kofler_, Apr 17 2022