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 A383960 #7 May 17 2025 08:14:54
%S A383960 0,1,1,2,1,2,1,2,2,2,1,3,1,2,2,2,1,3,1,3,2,2,1,3,2,2,2,3,1,3,1,2,2,2,
%T A383960 2,4,1,2,2,3,1,3,1,3,3,2,1,3,2,3,2,3,1,3,2,3,2,2,1,4,1,2,3,4,2,3,1,3,
%U A383960 2,3,1,4,1,2,3,3,2,3,1,3,2,2,1,4,2,2,2
%N A383960 The number of prime powers p^e having the property that e is an infinitary divisor of the p-adic valuation of n.
%C A383960 First differs from A238949 at n = 64.
%C A383960 First differs from A383959 at n = 256.
%H A383960 Amiram Eldar, <a href="/A383960/b383960.txt">Table of n, a(n) for n = 1..10000</a>
%F A383960 Additive with a(p^e) = A037445(e).
%F A383960 Sum_{k=1..n} a(k) ~ n*(log(log(n)) + B - C + D), where B is Mertens's constant (A077761), C = Sum_{p prime} 1/p^2 (A085548), and D = Sum_{p prime, e>=2} (1-1/p)*A037445(e)/p^e = 0.92752481299257205938... .
%t A383960 f[p_, e_] := 2^DigitCount[e, 2, 1]; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n]; a[1] = 0; ff[p_, e_] := d[e]; a[n_] := Plus @@ ff @@@ FactorInteger[n]; Array[a, 100]
%o A383960 (PARI) d(n) = vecprod(apply(x -> 1 << hammingweight(x), factor(n)[, 2]));
%o A383960 a(n) = vecsum(apply(x -> d(x), factor(n)[, 2]));
%Y A383960 Cf. A037445, A085548, A238949, A383760, A383865, A383959.
%K A383960 nonn,easy
%O A383960 1,4
%A A383960 _Amiram Eldar_, May 16 2025