|
%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
|
