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A357879
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Number of divisors of n with the same sum of prime indices as their quotient. Central column of A321144, taking gaps as 0's.
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12
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1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0
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OFFSET
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1,12
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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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EXAMPLE
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The a(3600) = 5 divisors, their prime indices, and the prime indices of their quotients:
45: {2,2,3} * {1,1,1,1,3}
50: {1,3,3} * {1,1,1,2,2}
60: {1,1,2,3} * {1,1,2,3}
72: {1,1,1,2,2} * {1,3,3}
80: {1,1,1,1,3} * {2,2,3}
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MATHEMATICA
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sumprix[n_]:=Total[Cases[FactorInteger[n], {p_, k_}:>k*PrimePi[p]]];
Table[Length[Select[Divisors[n], sumprix[#]==sumprix[n]/2&]], {n, 100}]
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CROSSREFS
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Cf. A033879, A033880, A064914, A181819, A213074, A235130, A237258, A276107, A300061, A321144, A357975.
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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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