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A342400
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a(n) is the number of distinct sums of distinct unitary divisors of n.
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2
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1, 3, 3, 3, 3, 12, 3, 3, 3, 15, 3, 13, 3, 15, 15, 3, 3, 15, 3, 13, 15, 15, 3, 15, 3, 15, 3, 15, 3, 72, 3, 3, 15, 15, 15, 15, 3, 15, 15, 15, 3, 96, 3, 15, 15, 15, 3, 15, 3, 15, 15, 15, 3, 15, 15, 13, 15, 15, 3, 108, 3, 15, 15, 3, 15, 144, 3, 15, 15, 142, 3, 13
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) <= A034448(n) with equality if and only if n is a unitary practical number (A286652).
a(p^e) = 3 for a prime p and e >= 1.
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MATHEMATICA
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a[n_] := Module[{d = Select[Divisors[n], CoprimeQ[#, n/#] &], x, s, m, c}, m = Length[d]; s = Plus @@ d; c = Rest@CoefficientList[Series[Product[1 + x^d[[i]], {i, 1, m}], {x, 0, s}], x]; Count[c, _?(# > 0 &)]]; Array[a, 100]
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CROSSREFS
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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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