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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 (list; graph; refs; listen; history; text; internal format)
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: A109357 A283802 A082041 * 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

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Last modified October 28 04:43 EDT 2021. Contains 348313 sequences. (Running on oeis4.)