A118123 a(n) = number of k's such that prime(n+1) = prime(n) + (prime(n) mod k).

0, 0, 1, 0, 2, 1, 3, 2, 1, 3, 1, 2, 3, 2, 1, 1, 3, 2, 4, 3, 1, 4, 3, 3, 2, 5, 4, 7, 6, 2, 2, 2, 7, 2, 5, 2, 1, 2, 3, 1, 3, 3, 7, 6, 7, 2, 1, 2, 8, 7, 1, 3, 5, 4, 1, 1, 3, 2, 6, 5, 5, 3, 2, 3, 2, 2, 4, 2, 7, 6, 1, 6, 2, 1, 6, 3, 2, 2, 2, 5, 3, 2, 7, 3, 6, 3, 6, 2, 7, 6, 5, 2, 6, 5, 10, 3, 2, 3, 2, 2, 2, 3, 1, 9, 2

Offset

1,5

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = # { k>0 | prime(n+1) - prime(n) = prime(n) % k }, where p % k is the remainder of p divided by k.

Mathematica

f[n_] := If[n == 1, 0, Block[{p = Prime@n, np = Prime[n + 1]}, Length@Select[Divisors[2p - np], # >= np - p &]]]; Array[f, 105]
nk[n_]:=Count[Mod[n, Range[n-1]], _?(#==NextPrime[n]-n&)]; nk/@Prime[ Range[ 110]] (* Harvey P. Dale, May 27 2016 *)

Prog

(PARI) A118123(n)={my(d=prime(n+1)-n=prime(n)); sumdiv(n-d, k, k>d)}

Crossrefs

Cf. A117078, A117563.

Sequence in context: A209281 A240554 A107338 * A181743 A330727 A174737

Adjacent sequences: A118120 A118121 A118122 * A118124 A118125 A118126

Keyword

nonn

Author

Rémi Eismann and Robert G. Wilson v, May 12 2006

Extensions

Edited by M. F. Hasler, Nov 07 2009

Status

approved