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A316887
Numbers k whose partition numbers have more than k nontrivial divisors.
0
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
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
KEYWORD
nonn
AUTHOR
Pierandrea Formusa, Jul 15 2018
EXTENSIONS
a(35)-a(50) from Giovanni Resta, Jul 16 2018
STATUS
approved