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A366748
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Numbers k such that (sum of odd prime indices of k) = (sum of even prime indices of k).
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4
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1, 12, 70, 90, 112, 144, 286, 325, 462, 520, 525, 594, 646, 675, 832, 840, 1045, 1080, 1326, 1334, 1344, 1666, 1672, 1728, 1900, 2142, 2145, 2294, 2465, 2622, 2695, 2754, 3040, 3432, 3465, 3509, 3526, 3900, 3944, 4186, 4255, 4312, 4455, 4845, 4864, 4900, 4982
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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The terms together with their prime indices begin:
1: {}
12: {1,1,2}
70: {1,3,4}
90: {1,2,2,3}
112: {1,1,1,1,4}
144: {1,1,1,1,2,2}
286: {1,5,6}
325: {3,3,6}
462: {1,2,4,5}
520: {1,1,1,3,6}
525: {2,3,3,4}
594: {1,2,2,2,5}
646: {1,7,8}
675: {2,2,2,3,3}
832: {1,1,1,1,1,1,6}
840: {1,1,1,2,3,4}
For example, 525 has prime indices {2,3,3,4}, and 3+3 = 2+4, so 525 is in the sequence.
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Total[Select[prix[#], OddQ]]==Total[Select[prix[#], EvenQ]]&]
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CROSSREFS
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For prime factors instead of indices we have A019507.
Partitions of this type are counted by A239261.
These are the positions of zeros in A366749.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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