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A325798 Numbers with at most as many divisors as the sum of their prime indices.

%I A325798 #7 May 28 2019 19:38:50
%S A325798 3,5,7,9,10,11,13,14,15,17,19,21,22,23,25,26,27,28,29,31,33,34,35,37,
%T A325798 38,39,41,43,44,45,46,47,49,50,51,52,53,55,57,58,59,61,62,63,65,66,67,
%U A325798 68,69,70,71,73,74,75,76,77,78,79,81,82,83,85,86,87,88,89
%N A325798 Numbers with at most as many divisors as the sum of their prime indices.
%C A325798 First differs from the complement of A325781 in lacking 156.
%C A325798 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 A325798 The sequence of terms together with their prime indices begins:
%e A325798    3: {2}
%e A325798    5: {3}
%e A325798    7: {4}
%e A325798    9: {2,2}
%e A325798   10: {1,3}
%e A325798   11: {5}
%e A325798   13: {6}
%e A325798   14: {1,4}
%e A325798   15: {2,3}
%e A325798   17: {7}
%e A325798   19: {8}
%e A325798   21: {2,4}
%e A325798   22: {1,5}
%e A325798   23: {9}
%e A325798   25: {3,3}
%e A325798   26: {1,6}
%e A325798   27: {2,2,2}
%e A325798   28: {1,1,4}
%e A325798   29: {10}
%e A325798   31: {11}
%t A325798 Select[Range[100],DivisorSigma[0,#]<=Total[Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]*k]]&]
%Y A325798 Positions of nonpositive terms in A325794.
%Y A325798 Heinz numbers of the partitions counted by A325834.
%Y A325798 Cf. A000005, A002033, A056239, A112798, A299702.
%Y A325798 Cf. A325694, A325780, A325781, A325792, A325793, A325795, A325796, A325797.
%K A325798 nonn
%O A325798 1,1
%A A325798 _Gus Wiseman_, May 23 2019