This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A346696 #12 Aug 01 2021 02:49:04 %S A346696 1,1,6,4,3,5,2,2,7,88,16,64,4,343,25,81,23,22,21,245,450,755,75,688, %T A346696 225,740,4432,307,671,1055,18881,7119,1415,4571,1365,411,36005,5799, %U A346696 3466,1410,4319,5993,646,60775,4470,90780,34595,36805,77125,11051,2514,46045,32713,114479,109221,19322,571126 %N A346696 a(n) is the least positive k such that A000041(n) divides A000041(n+k), or 0 if no such k exists. %C A346696 Conjecture: a(n) > 0 for all n. %e A346696 a(7) = 2 because A000041(7) = 15 divides A000041(9) = 30. %t A346696 a[n_]:=(k=1;While[!Divisible[PartitionsP[n+k],PartitionsP@n],k++];k);Array[a,30,0] (* _Giorgos Kalogeropoulos_, Jul 29 2021 *) %o A346696 (PARI) a(n)=my(t=1); while(numbpart(n+t)%numbpart(n), t++); t %Y A346696 Cf. A000041, A079031. %K A346696 nonn %O A346696 0,3 %A A346696 _Altug Alkan_, Jul 29 2021