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A304409 If n = Product (p_j^k_j) then a(n) = Product (p_j*(k_j + 1)). 6
1, 4, 6, 6, 10, 24, 14, 8, 9, 40, 22, 36, 26, 56, 60, 10, 34, 36, 38, 60, 84, 88, 46, 48, 15, 104, 12, 84, 58, 240, 62, 12, 132, 136, 140, 54, 74, 152, 156, 80, 82, 336, 86, 132, 90, 184, 94, 60, 21, 60, 204, 156, 106, 48, 220, 112, 228, 232, 118, 360, 122, 248, 126, 14, 260 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Ilya Gutkovskiy, Scatter plot of a(n) up to n=50000

Index entries for sequences computed from indices in prime factorization

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = A000005(n)*A007947(n).

a(p^k) = p*(k + 1) where p is a prime and k > 0.

a(n) = 2^omega(n)*n if n is a squarefree (A005117), where omega() = A001221.

EXAMPLE

a(12) = a(2^2*3) = 2*(2 + 1) * 3*(1 + 1) = 36.

MATHEMATICA

a[n_] := Times @@ (#[[1]] (#[[2]] + 1) & /@ FactorInteger[n]); a[1] = 1; Table[a[n], {n, 65}]

Table[DivisorSigma[0, n] Last[Select[Divisors[n], SquareFreeQ]], {n, 65}]

PROG

(PARI) a(n)={numdiv(n)*factorback(factorint(n)[, 1])} \\ Andrew Howroyd, Jul 24 2018

CROSSREFS

Cf. A000005, A000026, A000040, A001221, A005117, A007947, A016754 (numbers n such that a(n) is odd), A034444, A038040, A064549, A299822, A304407, A304408, A304410 (fixed points), A304411, A304412.

Sequence in context: A267573 A345282 A193814 * A081732 A079033 A272771

Adjacent sequences:  A304406 A304407 A304408 * A304410 A304411 A304412

KEYWORD

nonn,mult

AUTHOR

Ilya Gutkovskiy, May 12 2018

STATUS

approved

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Last modified August 11 22:58 EDT 2022. Contains 356067 sequences. (Running on oeis4.)