A316887 Numbers k whose partition numbers have more than k nontrivial divisors.

21, 75, 94, 96, 97, 109, 124, 125, 128, 129, 131, 136, 149, 180, 213, 327, 334, 347, 358, 374, 424, 434, 449, 481, 581, 644, 699, 765, 776, 789, 859, 896, 974, 999, 1216, 1240, 1243, 1249, 1267, 1269, 1324, 1398, 1442, 1499, 1524, 1587, 1685, 1699, 1752, 1779

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

21 belongs to this sequence as the partition number of 21 is 792, which has 22 nontrivial divisors (divisors different from 1 and itself), and 22 > 21.

Mathematica

Select[Range[1000], DivisorSigma[0, PartitionsP[#]] > # + 2 &] (* or *) First/@ Select[ Import[ "https://oeis.org/A085543/b085543.txt", "Table"], #[[2]] > #[[1]] + 2&] (* Giovanni Resta, Jul 16 2018 *)

Prog

(PARI) select(n->numdiv(numbpart(n))-2 > n, [1..1000]) \\ Andrew Howroyd, Jul 15 2018
(Sage)
r=""
for i in range(1000):
   l=Partitions(i+1).cardinality().divisors()
   if ((len(l)-2)>i+1): r=r+str(i+1)+", "
print(r)

Crossrefs

Cf. A000005, A000041, A085543.

Sequence in context: A283802 A082041 A350160 * A296155 A218960 A218955

Adjacent sequences: A316884 A316885 A316886 * A316888 A316889 A316890

Keyword

nonn

Author

Pierandrea Formusa, Jul 15 2018

Extensions

a(35)-a(50) from Giovanni Resta, Jul 16 2018

Status

approved