A226957 Number of prime divisors p of 2n such that p-1 divides n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2

Offset: 1

Author

José María Grau Ribas, Jun 24 2013

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A136141.

Programs

Mathematica

fa = FactorInteger; a[n_] := Sum[If[IntegerQ[n/(fa[2 n][[i,1]]-1)],1,0],{i, Length[fa[2 n]]}]; Table[a[n], {n, 1, 100}]

PARI

a(n)=my(f=factor(2*n)[,1]);sum(i=1,#f,n%(f[i]-1)==0) \\ Charles R Greathouse IV, Jun 26 2013

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/2 + Sum_{p prime} 1/(p*(p-1)) = 1/2 + A136141 = 1.273156669... . - Amiram Eldar, May 17 2024

Extensions

Erroneous a(87) added by T. D. Noe, corrected by Charles R Greathouse IV, Jun 26 2013