A088850 Number of different values of k when A056239(k) = A056239(k+1) = n.

0, 0, 1, 1, 1, 1, 2, 1, 0, 4, 0, 1, 3, 1, 4, 2, 1, 3, 0, 3, 2, 4, 3, 3, 2, 5, 4, 6, 11, 2, 6, 5, 8, 8, 7, 7, 12, 14, 8, 8, 10, 7, 10, 11, 11, 11, 20, 17, 30, 19, 22, 16, 22, 21, 17, 26, 30, 27, 30, 22, 23, 35, 35, 26, 28, 32, 49, 28, 50, 45, 51, 56, 44, 43, 49

Offset: 0

Author

Naohiro Nomoto, Nov 24 2003

Keywords

• nonn

Comments

Also the number of different values k, such that both k and k+1 occur in row n of A215366. - Alois P. Heinz, Aug 09 2012

Links

• Amiram Eldar, Table of n, a(n) for n = 0..98

Crossrefs

Cf. A056239, A215366.

Programs

Mathematica

a[n_] := Count[Differences[Sort[Times @@@ (Prime /@ IntegerPartitions[n])]], 1]; Array[a, 51, 0] (* Amiram Eldar, Jun 18 2025 *)

PARI

a(n) = {my(v = List(), c = 0); forpart(p = n, listput(v, vecprod(apply(prime, Vec(p))))); v = vecsort(v); for(i = 1, #v-1, if(v[i+1] == v[i] + 1, c++)); c;} \\ Amiram Eldar, Jun 18 2025

Extensions

a(16)-a(20) from R. J. Mathar, Sep 27 2011

a(21)-a(50) from Alois P. Heinz, Aug 09 2012

a(51)-a(74) from Amiram Eldar, Jun 18 2025