A343068 Multiplicative with a(p^e) = e*a(p-1).

1, 1, 1, 2, 2, 1, 1, 3, 2, 2, 2, 2, 2, 1, 2, 4, 4, 2, 2, 4, 1, 2, 2, 3, 4, 2, 3, 2, 2, 2, 2, 5, 2, 4, 2, 4, 4, 2, 2, 6, 6, 1, 1, 4, 4, 2, 2, 4, 2, 4, 4, 4, 4, 3, 4, 3, 2, 2, 2, 4, 4, 2, 2, 6, 4, 2, 2, 8, 2, 2, 2, 6, 6, 4, 4, 4, 2, 2, 2, 8, 4, 6, 6, 2, 8, 1

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(2^n) = n*a(2-1) = n.

Example

a(2) = a(2-1) = 1; a(3) = a(3-1) = 1.

Maple

a:= proc(n) option remember; `if`(n=1, 1,
      mul(i[2]*a(i[1]-1), i=ifactors(n)[2]))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 04 2021

Mathematica

a[1] = 1; a[p_, s_]:= a[p, s]=s a[p-1];
a[n_]:=a[n]= Module[{aux = FactorInteger[n]}, Product[a[aux[[i, 1]], aux[[i, 2]]], {i, Length[aux]}]]; Table[a[n], {n, 100}]

Prog

(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = f[k, 2]*a(f[k, 1]-1); f[k, 2] = 1); factorback(f); \\ Michel Marcus, Apr 23 2021

Crossrefs

Cf. A279513, A191614.

Sequence in context: A175062 A139767 A207822 * A370489 A057555 A075532

Adjacent sequences: A343065 A343066 A343067 * A343069 A343070 A343071

Keyword

nonn,mult

Author

José María Grau Ribas, Apr 04 2021

Status

approved