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 A348341 #17 Feb 16 2025 08:34:02
%S A348341 0,0,0,1,0,0,0,0,1,0,0,2,0,0,0,3,0,2,0,2,0,0,0,0,1,0,0,2,0,0,0,2,0,0,
%T A348341 0,5,0,0,0,0,0,0,0,2,2,0,0,6,1,2,0,2,0,0,0,0,0,0,0,4,0,0,2,3,0,0,0,2,
%U A348341 0,0,0,4,0,0,2,2,0,0,0,6,3,0,0,4,0,0,0
%N A348341 a(n) is the number of noninfinitary divisors of n.
%H A348341 Amiram Eldar, <a href="/A348341/b348341.txt">Table of n, a(n) for n = 1..10000</a>
%H A348341 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/InfinitaryDivisor.html">Infinitary Divisor</a>.
%F A348341 a(n) = A000005(n) - A037445(n).
%F A348341 a(n) = 0 if and only if the number of divisors of n is a power of 2, (i.e., n is in A036537).
%F A348341 a(n) > 0 if and only if the number of divisors of n is not a power of 2, (i.e., n is in A162643).
%F A348341 Sum_{k=1..n} a(k) ~ c * n * log(n), where c = (1 - 2 * A327576) = 0.266749... . - _Amiram Eldar_, Dec 09 2022
%e A348341 a(4) = 1 since 4 has one noninfinitary divisor, 2.
%t A348341 a[1] = 0; a[n_] := DivisorSigma[0, n] - Times @@ Flatten[2^DigitCount[#, 2, 1] & /@ FactorInteger[n][[;; , 2]]]; Array[a, 100]
%o A348341 (PARI) A348341(n) = (numdiv(n)-factorback(apply(a -> 2^hammingweight(a), factorint(n)[, 2]))); \\ _Antti Karttunen_, Oct 13 2021
%Y A348341 Cf. A000005, A036537, A037445, A077609, A162643, A327576, A348271.
%Y A348341 Similar sequences: A034444, A048105, A286324, A049419.
%K A348341 nonn
%O A348341 1,12
%A A348341 _Amiram Eldar_, Oct 13 2021