cp's OEIS Frontend

A325795 Numbers with more divisors than the sum of their prime indices.

%I A325795 #4 May 23 2019 14:51:46
%S A325795 1,2,4,6,8,12,16,18,20,24,30,32,36,40,42,48,54,56,60,64,72,80,84,90,
%T A325795 96,100,108,112,120,126,128,132,140,144,150,156,160,162,168,176,180,
%U A325795 192,198,200,204,210,216,220,224,234,240,252,256,260,264,270,280,288
%N A325795 Numbers with more divisors than the sum of their prime indices.
%C A325795 First differs from A325781 in having 156.
%C A325795 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798, with sum A056239(n).
%e A325795 The sequence of terms together with their prime indices begins:
%e A325795     1: {}
%e A325795     2: {1}
%e A325795     4: {1,1}
%e A325795     6: {1,2}
%e A325795     8: {1,1,1}
%e A325795    12: {1,1,2}
%e A325795    16: {1,1,1,1}
%e A325795    18: {1,2,2}
%e A325795    20: {1,1,3}
%e A325795    24: {1,1,1,2}
%e A325795    30: {1,2,3}
%e A325795    32: {1,1,1,1,1}
%e A325795    36: {1,1,2,2}
%e A325795    40: {1,1,1,3}
%e A325795    42: {1,2,4}
%e A325795    48: {1,1,1,1,2}
%e A325795    54: {1,2,2,2}
%e A325795    56: {1,1,1,4}
%e A325795    60: {1,1,2,3}
%e A325795    64: {1,1,1,1,1,1}
%t A325795 Select[Range[100],DivisorSigma[0,#]>Total[Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]*k]]&]
%Y A325795 Positions of positive terms in A325794.
%Y A325795 Heinz numbers of the partitions counted by A325831.
%Y A325795 Cf. A000005, A002033, A056239, A112798, A299702.
%Y A325795 Cf. A325694, A325780, A325781, A325792, A325793, A325796, A325797, A325798.
%K A325795 nonn
%O A325795 1,2
%A A325795 _Gus Wiseman_, May 23 2019