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 A381733 #9 Mar 15 2025 04:33:10 %S A381733 1,1,1,2,2,1,1,1,1,2,1,3,2,2,1,1,1,2,1,3,2,2,1,2,2,1,1,4,2,3,1,2,2,2, %T A381733 2,4,2,2,2,2,2,1,1,3,1,2,1,1,0,2,1,3,1,2,2,3,2,2,1,5,2,1,2,2,4,3,1,4, %U A381733 2,3,1,3,2,1,1,4,2,2,1,2,1,2,1,5,3,2,1,2,1,4,1,4,2,2,2,2,1,1,2,4 %N A381733 Number of divisors d of n such that 2^omega(n + d) = tau(n + d), where omega = A001221 and tau = A000005. %t A381733 a[n_]:=Length[Select[Divisors[n], DivisorSigma[0, #+n]==2^PrimeNu[#+n]&]]; Array[a,100] (* _Stefano Spezia_, Mar 07 2025 *) %o A381733 (Magma) [#[d: d in Divisors(n) | 2^#PrimeDivisors(n+d) eq #Divisors(n+d)]: n in [1..100]]; %Y A381733 Cf. A000005, A001221, A005117, A381136, A381138. %K A381733 nonn %O A381733 1,4 %A A381733 _Juri-Stepan Gerasimov_, Mar 05 2025