A241564 Number of 3-element subsets of {1,...,n} whose sum has more than 3 divisors.

0, 0, 1, 2, 6, 11, 22, 35, 55, 78, 110, 145, 192, 245, 312, 386, 476, 572, 684, 804, 943, 1091, 1261, 1442, 1647, 1864, 2108, 2366, 2651, 2951, 3281, 3629, 4010, 4410, 4845, 5299, 5790, 6301, 6850, 7420, 8031, 8665, 9342, 10043, 10788, 11559, 12375, 13215

Offset

1,4

Comments

If the constraint on the number of divisors is dropped, one gets A000292 = tetrahedral numbers C(n+2,3) = n*(n+1)*(n+2)/6, which therefore is an upper bound.

If the subsets with more than 2 divisors are counted, one gets A241563.

Links

Robert Israel, Table of n, a(n) for n = 1..5000

W. E. Clark in reply to A. Hatzipolakis, A generalization, SeqFan list, Apr 24 2014

Maple

N:= 100: # for a(1)..a(N)
t:= 0: R:= NULL:
for n from 1 to N do
  v:= select(s -> numtheory:-tau(s+n)>3, [$2..2*n-3]);
  t:= t + add(floor((s-1)/2) - max(0, s-n) , s = v);
  R:= R, t;
od:
R; # Robert Israel, Jan 04 2021

Prog

(PARI) a(n, m=3, d=3)={s=0; u=vector(m, n, 1)~; forvec(v=vector(m, i, [1, n]), numdiv(v*u)>d&&s++, 2); s}

Crossrefs

Sequence in context: A085571 A007684 A296557 * A135348 A305101 A363936

Adjacent sequences: A241561 A241562 A241563 * A241565 A241566 A241567

Keyword

nonn

Author

M. F. Hasler, Apr 25 2014

Status

approved