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A049599
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Number of (1+e)-divisors of n: if n = Product p(i)^r(i), d = Product p(i)^s(i) and s(i) = 0 or s(i) divides r(i), then d is a (1+e)-divisor of n.
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18
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1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 4, 2, 6, 2, 6, 4, 4, 2, 6, 3, 4, 3, 6, 2, 8, 2, 3, 4, 4, 4, 9, 2, 4, 4, 6, 2, 8, 2, 6, 6, 4, 2, 8, 3, 6, 4, 6, 2, 6, 4, 6, 4, 4, 2, 12, 2, 4, 6, 5, 4, 8, 2, 6, 4, 8, 2, 9, 2, 4, 6, 6, 4, 8, 2, 8, 4, 4, 2, 12, 4, 4, 4, 6, 2, 12, 4, 6, 4, 4, 4, 6, 2, 6, 6, 9, 2, 8, 2
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OFFSET
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1,2
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COMMENTS
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A divisor of n is a (1+e)-divisor if and only if it is a unitary divisor of an exponential divisor of n (see A077610 and A322791). - Amiram Eldar, Feb 26 2024
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LINKS
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FORMULA
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If n = Product p(i)^r(i) then a(n) = Product (tau(r(i))+1), where tau(n) = number of divisors of n, cf. A000005. - Vladeta Jovovic, Apr 29 2001
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MATHEMATICA
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a[n_] := Times @@ (DivisorSigma[0, #] + 1 &) /@ FactorInteger[n][[All, 2]]; a[1] = 1; Table[a[n], {n, 1, 103}] (* Jean-François Alcover, Oct 10 2011 *)
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PROG
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(Haskell)
a049599 = product . map ((+ 1) . a000005 . fromIntegral) . a124010_row
(PARI) a(n) = vecprod(apply(x->numdiv(x)+1, factor(n)[, 2])); \\ Amiram Eldar, Aug 13 2023
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CROSSREFS
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KEYWORD
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nonn,easy,nice,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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