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A328892 If n = Product (p_j^k_j) then a(n) = Sum (2^(k_j - 1)). 0
0, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 3, 1, 2, 2, 8, 1, 3, 1, 3, 2, 2, 1, 5, 2, 2, 4, 3, 1, 3, 1, 16, 2, 2, 2, 4, 1, 2, 2, 5, 1, 3, 1, 3, 3, 2, 1, 9, 2, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 4, 1, 2, 3, 32, 2, 3, 1, 3, 2, 3, 1, 6, 1, 2, 3, 3, 2, 3, 1, 9, 8, 2, 1, 4, 2, 2, 2, 5, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
FORMULA
If n = Product (p_j^k_j) then a(n) = Sum ordered partition(k_j).
Additive with a(p^e) = 2^(e-1).
EXAMPLE
a(72) = 6 because 72 = 2^3 * 3^2 and 2^(3 - 1) + 2^(2 - 1) = 6.
MAPLE
a:= n-> add(2^(i[2]-1), i=ifactors(n)[2]):
seq(a(n), n=1..100); # Alois P. Heinz, Oct 29 2019
MATHEMATICA
a[1] = 0; a[n_] := Plus @@ (2^(#[[2]] - 1) & /@ FactorInteger[n]); Table[a[n], {n, 1, 90}]
PROG
(PARI) a(n)={vecsum([2^(k-1) | k<-factor(n)[, 2]])} \\ Andrew Howroyd, Oct 29 2019
CROSSREFS
Cf. A000040 (positions of 1's), A008481, A011782, A162510, A324910.
Sequence in context: A216506 A072342 A257089 * A296131 A345344 A319004
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 29 2019
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)