A351867 Heptagonal numbers which are products of four distinct primes.

3010, 4774, 10465, 14326, 20566, 28462, 54538, 59059, 59830, 66178, 66994, 87142, 104755, 112042, 120670, 121771, 131905, 137710, 138886, 168610, 179158, 201214, 212722, 223054, 249166, 273406, 288490, 290191, 314530, 343546, 358534, 375778, 401401, 405418, 419635, 461605

Offset

1,1

Comments

A squarefree subsequence of heptagonal numbers.

Links

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

Example

3010 = 2*5*7*43 = 35(5*35-3)/2.
4774 = 2*7*11*31 = 44(5*44-3)/2.
10465 = 5*7*13*23 = 65(5*65-3)/2.
14326 = 2*13*19*29 = 76(5*76-3)/2.

Maple

R:= NULL: count:= 0:
for n from 1 while count < 100 do
  x:= n*(5*n-3)/2;
  F:= ifactors(x)[2];
  if F[.., 2] = [1, 1, 1, 1] then count:= count+1; R:= R, x;  fi
od:
R; # Robert Israel, Oct 28 2025

Prog

(Python)
from itertools import count, islice
from sympy import factorint
def A351867_gen(): return filter(lambda k:sum((f := factorint(k)).values()) == 4 == len(f), (n*(5*n-3)//2 for n in count(1)))
A351867_list = list(islice(A351867_gen(), 20)) # Chai Wah Wu, Apr 14 2022

Crossrefs

Intersection of A000566 and A046386.

Sequence in context: A279584 A004228 A004229 * A004230 A162606 A233963

Adjacent sequences: A351864 A351865 A351866 * A351868 A351869 A351870

Keyword

nonn

Author

Massimo Kofler, Apr 12 2022

Status

approved