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A333267 If n = Product (p_j^k_j) then a(n) = Product (a(pi(p_j)) * k_j), where pi = A000720. 1
1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 2, 1, 2, 1, 4, 2, 2, 3, 2, 2, 1, 2, 3, 2, 1, 3, 4, 1, 1, 1, 5, 1, 2, 2, 4, 2, 3, 1, 3, 1, 2, 2, 2, 2, 2, 1, 4, 4, 2, 2, 2, 4, 3, 1, 6, 3, 1, 2, 2, 2, 1, 4, 6, 1, 1, 3, 4, 2, 2, 2, 6, 2, 2, 2, 6, 2, 1, 1, 4, 4, 1, 2, 4, 2, 2, 1, 3, 3, 2, 2, 4, 1, 1, 3, 5, 2, 4, 2, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..65536

Index entries for sequences computed from indices in prime factorization

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = A005361(n) * Product_{p|n, p prime} a(pi(p)).

a(n) = a(prime(n)).

a(p^k) = k * a(p), where p is prime.

a(A002110(n)) = Product_{k=1..n} a(k).

EXAMPLE

a(36) = a(2^2 * 3^2) = a(prime(1)^2 * prime(2)^2) = a(1) * 2 * a(2) * 2 = 4.

MAPLE

a:= proc(n) option remember;

      mul(a(numtheory[pi](i[1]))*i[2], i=ifactors(n)[2])

    end:

seq(a(n), n=1..120);  # Alois P. Heinz, Mar 13 2020

MATHEMATICA

a[1] = 1; a[n_] := a[n] = Times @@ (a[PrimePi[#[[1]]]] #[[2]] & /@ FactorInteger[n]); Table[a[n], {n, 1, 100}]

CROSSREFS

Cf. A000026, A000720, A002110, A003963, A005361, A054725, A109129, A276625 (positions of 1's), A282446, A304117, A318046, A328880.

Sequence in context: A122563 A204030 A234503 * A236325 A080345 A285202

Adjacent sequences:  A333264 A333265 A333266 * A333268 A333269 A333270

KEYWORD

nonn,mult

AUTHOR

Ilya Gutkovskiy, Mar 13 2020

STATUS

approved

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Last modified October 30 05:44 EDT 2020. Contains 338077 sequences. (Running on oeis4.)