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 A118123 a(n) = number of k's such that prime(n+1) = prime(n) + (prime(n) mod k). 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 15 11:01 EDT 2024. Contains 374332 sequences. (Running on oeis4.)