A341041 If n = Product (p_j^k_j) then a(n) = 1 + Product (a(pi(p_j))), where pi = A000720, with a(1) = 1.

1, 2, 3, 2, 4, 3, 3, 2, 3, 4, 5, 3, 4, 3, 7, 2, 4, 3, 3, 4, 5, 5, 4, 3, 4, 4, 3, 3, 5, 7, 6, 2, 9, 4, 7, 3, 4, 3, 7, 4, 5, 5, 4, 5, 7, 4, 8, 3, 3, 4, 7, 4, 3, 3, 13, 3, 5, 5, 5, 7, 4, 6, 5, 2, 10, 9, 4, 4, 7, 7, 5, 3, 6, 4, 7, 3, 9, 7, 6, 4, 3, 5, 5, 5, 10, 4, 9, 5, 4, 7, 7, 4, 11, 8, 7, 3, 5, 3, 9, 4

Offset

1,2

Links

Table of n, a(n) for n=1..100.

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = a(prime(n)^k) - 1 for k > 0.

a(2*n) = a(n) for n > 1.

Example

a(45) = a(3^2 * 5) = a(prime(2)^2 * prime(3)) = 1 + a(2) * a(3) = 1 + 2 * 3 = 7.

Maple

a:= n-> `if`(n=1, 1, 1+mul(a(numtheory[pi](i[1])), i=ifactors(n)[2])):
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 03 2021

Mathematica

a[1] = 1; a[n_] := a[n] = 1 + Times @@ (a[PrimePi[#[[1]]]] & /@ FactorInteger[n]); Table[a[n], {n, 100}]

Crossrefs

Cf. A000720, A093320, A156061, A214567, A328880.

Sequence in context: A358667 A358552 A317713 * A361660 A318046 A246348

Adjacent sequences: A341038 A341039 A341040 * A341042 A341043 A341044

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 03 2021

Status

approved