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

Author

José María Grau Ribas, Apr 04 2021

Keywords

• nonn
• mult

Examples

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

Links

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

Crossrefs

Cf. A279513, A191614.

Programs

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}]

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

Formula

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