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

Author

Pierandrea Formusa, Jul 15 2018

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000005, A000041, A085543.

Programs

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 *)

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)

Extensions

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