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

1,6

Links

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

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

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}]

Prog

(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

Crossrefs

Cf. A136141.

Sequence in context: A347447 A107577 A073700 * A108775 A300826 A373126

Adjacent sequences: A226954 A226955 A226956 * A226958 A226959 A226960

Keyword

nonn,easy

Author

José María Grau Ribas, Jun 24 2013

Extensions

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

Status

approved