A345699 Multiplicative with a(p) = a(p-1) and a(p^e) = a(p) + a(e) if e>1.

1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 3, 3, 2, 2, 4, 1, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 4, 4, 2, 2, 4, 4, 1, 1, 4, 4, 2, 2, 3, 2, 3, 3, 4, 4, 2, 4, 2, 2, 2, 2, 4, 4, 2, 2, 2, 4, 2, 2, 6, 2, 2, 2, 4, 4, 4, 3, 4, 2, 2, 2, 6, 3, 4, 4, 2, 6, 1, 2

Offset

1,4

Links

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

Example

a(11)=a(10)=a(5)*a(2); a(2)=1; a(5)=a(4)=a(2)+a(2)=2; so a(11)=2.

Maple

a:= proc(n) option remember; mul(`if`(i[2]=1,
      a(i[1]-1), a(i[1])+a(i[2])), i=ifactors(n)[2])
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 28 2021

Mathematica

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

Prog

(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = a(f[k, 1]-1); if (f[k, 2] > 1, f[k, 1] += a(f[k, 2])); f[k, 2] = 1); factorback(f); \\ Michel Marcus, Jun 26 2021

Crossrefs

Cf. A343068, A345763.

Sequence in context: A254687 A182590 A047846 * A212632 A359477 A025885

Adjacent sequences: A345696 A345697 A345698 * A345700 A345701 A345702

Keyword

nonn,mult

Author

José María Grau Ribas, Jun 24 2021

Status

approved