

A360953


Numbers whose right half of prime indices (exclusive) adds up to half the total sum of prime indices.


5



1, 4, 9, 12, 16, 25, 30, 48, 49, 63, 64, 70, 81, 108, 121, 154, 165, 169, 192, 256, 270, 273, 286, 289, 325, 361, 442, 529, 561, 567, 595, 625, 646, 675, 729, 741, 750, 768, 841, 874, 931, 961, 972, 1024, 1045, 1173, 1334, 1369, 1495, 1575, 1653, 1681, 1750
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OFFSET

1,2


COMMENTS

Also numbers whose left half of prime indices (inclusive) adds up to half the total sum of prime indices.
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.


LINKS



EXAMPLE

The terms together with their prime indices begin:
1: {}
4: {1,1}
9: {2,2}
12: {1,1,2}
16: {1,1,1,1}
25: {3,3}
30: {1,2,3}
48: {1,1,1,1,2}
49: {4,4}
63: {2,2,4}
64: {1,1,1,1,1,1}
70: {1,3,4}
81: {2,2,2,2}
108: {1,1,2,2,2}
For example, the prime indices of 1575 are {2,2,3,3,4}, with right half (exclusive) {3,4}, with sum 7, and the total sum of prime indices is 14, so 1575 is in the sequence.


MATHEMATICA

Select[Range[100], With[{w=Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]}, Total[Take[w, Floor[Length[w]/2]]]==Total[w]/2]&]


CROSSREFS

These partitions are counted by A360674.
The left inclusive version is A360953 (this sequence).
First for prime indices, second for partitions, third for prime factors:


KEYWORD

nonn


AUTHOR



STATUS

approved



