A325797 - OEIS

%I #4 May 23 2019 14:49:38

%S 5,7,9,11,13,14,15,17,19,21,22,23,25,26,27,29,31,33,34,35,37,38,39,41,

%T 43,44,45,46,47,49,50,51,52,53,55,57,58,59,61,62,63,65,67,68,69,71,73,

%U 74,75,76,77,78,79,81,82,83,85,86,87,89,91,92,93,94,95,97

%N Numbers with fewer divisors than the sum of their prime indices.

%C 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 The sequence of terms together with their prime indices begins:

%e    5: {3}

%e    7: {4}

%e    9: {2,2}

%e   11: {5}

%e   13: {6}

%e   14: {1,4}

%e   15: {2,3}

%e   17: {7}

%e   19: {8}

%e   21: {2,4}

%e   22: {1,5}

%e   23: {9}

%e   25: {3,3}

%e   26: {1,6}

%e   27: {2,2,2}

%e   29: {10}

%e   31: {11}

%e   33: {2,5}

%e   34: {1,7}

%e   35: {3,4}

%t Select[Range[100],DivisorSigma[0,#]<Total[Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]*k]]&]

%Y Positions of negative terms in A325794.

%Y Heinz numbers of the partitions counted by A325833.

%Y Cf. A000005, A002033, A056239, A112798, A299702.

%Y Cf. A325694, A325780, A325781, A325792, A325793, A325795, A325796, A325798.

%K nonn

%O 1,1

%A _Gus Wiseman_, May 23 2019