A325795 - OEIS

%I #4 May 23 2019 14:51:46

%S 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 96,100,108,112,120,126,128,132,140,144,150,156,160,162,168,176,180,

%U 192,198,200,204,210,216,220,224,234,240,252,256,260,264,270,280,288

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

%C First differs from A325781 in having 156.

%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     1: {}

%e     2: {1}

%e     4: {1,1}

%e     6: {1,2}

%e     8: {1,1,1}

%e    12: {1,1,2}

%e    16: {1,1,1,1}

%e    18: {1,2,2}

%e    20: {1,1,3}

%e    24: {1,1,1,2}

%e    30: {1,2,3}

%e    32: {1,1,1,1,1}

%e    36: {1,1,2,2}

%e    40: {1,1,1,3}

%e    42: {1,2,4}

%e    48: {1,1,1,1,2}

%e    54: {1,2,2,2}

%e    56: {1,1,1,4}

%e    60: {1,1,2,3}

%e    64: {1,1,1,1,1,1}

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

%Y Positions of positive terms in A325794.

%Y Heinz numbers of the partitions counted by A325831.

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

%Y Cf. A325694, A325780, A325781, A325792, A325793, A325796, A325797, A325798.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 23 2019