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%I #18 Jul 30 2018 13:21:35
%S 21,75,94,96,97,109,124,125,128,129,131,136,149,180,213,327,334,347,
%T 358,374,424,434,449,481,581,644,699,765,776,789,859,896,974,999,1216,
%U 1240,1243,1249,1267,1269,1324,1398,1442,1499,1524,1587,1685,1699,1752,1779
%N Numbers k whose partition numbers have more than k nontrivial divisors.
%e 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.
%t 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 *)
%o (PARI) select(n->numdiv(numbpart(n))-2 > n, [1..1000]) \\ _Andrew Howroyd_, Jul 15 2018
%o (Sage)
%o r=""
%o for i in range(1000):
%o l=Partitions(i+1).cardinality().divisors()
%o if ((len(l)-2)>i+1): r=r+str(i+1)+","
%o print(r)
%Y Cf. A000005, A000041, A085543.
%K nonn
%O 1,1
%A _Pierandrea Formusa_, Jul 15 2018
%E a(35)-a(50) from _Giovanni Resta_, Jul 16 2018
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