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 A226957 #29 May 17 2024 03:15:59
%S A226957 1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,1,
%T A226957 1,2,1,1,1,2,1,3,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1,1,2,1,1,
%U A226957 1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,3,1,1,1,1,1,2
%N A226957 Number of prime divisors p of 2n such that p-1 divides n.
%H A226957 Charles R Greathouse IV, <a href="/A226957/b226957.txt">Table of n, a(n) for n = 1..10000</a>
%F A226957 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/2 + Sum_{p prime} 1/(p*(p-1)) = 1/2 + A136141 = 1.273156669... . - _Amiram Eldar_, May 17 2024
%t A226957 fa = FactorInteger; a[n_] := Sum[If[IntegerQ[n/(fa[2 n][[i,1]]-1)],1,0],{i, Length[fa[2 n]]}]; Table[a[n], {n, 1, 100}]
%o A226957 (PARI) a(n)=my(f=factor(2*n)[,1]);sum(i=1,#f,n%(f[i]-1)==0) \\ _Charles R Greathouse IV_, Jun 26 2013
%Y A226957 Cf. A136141.
%K A226957 nonn,easy
%O A226957 1,6
%A A226957 _José María Grau Ribas_, Jun 24 2013
%E A226957 Erroneous a(87) added by _T. D. Noe_, corrected by _Charles R Greathouse IV_, Jun 26 2013