A346696 a(n) is the least positive k such that A000041(n) divides A000041(n+k), or 0 if no such k exists.

1, 1, 6, 4, 3, 5, 2, 2, 7, 88, 16, 64, 4, 343, 25, 81, 23, 22, 21, 245, 450, 755, 75, 688, 225, 740, 4432, 307, 671, 1055, 18881, 7119, 1415, 4571, 1365, 411, 36005, 5799, 3466, 1410, 4319, 5993, 646, 60775, 4470, 90780, 34595, 36805, 77125, 11051, 2514, 46045, 32713, 114479, 109221, 19322, 571126

Offset: 0

Author

Altug Alkan, Jul 29 2021

Keywords

• nonn

Comments

Conjecture: a(n) > 0 for all n.

Examples

			a(7) = 2 because A000041(7) = 15 divides A000041(9) = 30.
		

Crossrefs

Cf. A000041, A079031.

Programs

Mathematica

a[n_]:=(k=1;While[!Divisible[PartitionsP[n+k],PartitionsP@n],k++];k);Array[a,30,0] (* Giorgos Kalogeropoulos, Jul 29 2021 *)

PARI

a(n)=my(t=1); while(numbpart(n+t)%numbpart(n), t++); t