cp's OEIS Frontend

A325796 Numbers with at least as many divisors as the sum of their prime indices.

%I A325796 #5 May 23 2019 14:51:35
%S A325796 1,2,3,4,6,8,10,12,16,18,20,24,28,30,32,36,40,42,48,54,56,60,64,66,70,
%T A325796 72,80,84,88,90,96,100,108,112,120,126,128,132,140,144,150,156,160,
%U A325796 162,168,176,180,192,198,200,204,208,210,216,220,224,228,234,240
%N A325796 Numbers with at least as many divisors as the sum of their prime indices.
%C A325796 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 A325796 The sequence of terms together with their prime indices begins:
%e A325796     1: {}
%e A325796     2: {1}
%e A325796     3: {2}
%e A325796     4: {1,1}
%e A325796     6: {1,2}
%e A325796     8: {1,1,1}
%e A325796    10: {1,3}
%e A325796    12: {1,1,2}
%e A325796    16: {1,1,1,1}
%e A325796    18: {1,2,2}
%e A325796    20: {1,1,3}
%e A325796    24: {1,1,1,2}
%e A325796    28: {1,1,4}
%e A325796    30: {1,2,3}
%e A325796    32: {1,1,1,1,1}
%e A325796    36: {1,1,2,2}
%e A325796    40: {1,1,1,3}
%e A325796    42: {1,2,4}
%e A325796    48: {1,1,1,1,2}
%e A325796    54: {1,2,2,2}
%t A325796 Select[Range[100],DivisorSigma[0,#]>=Total[Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]*k]]&]
%Y A325796 Positions of nonnegative terms in A325794.
%Y A325796 Heinz numbers of the partitions counted by A325832.
%Y A325796 Cf. A000005, A002033, A056239, A112798, A299702.
%Y A325796 Cf. A325694, A325780, A325781, A325792, A325793, A325795, A325797, A325798.
%K A325796 nonn
%O A325796 1,2
%A A325796 _Gus Wiseman_, May 23 2019