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 A383959 #9 May 17 2025 08:15:10
%S A383959 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 A383959 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 A383959 2,3,1,4,1,2,3,3,2,3,1,3,2,2,1,4,2,2,2
%N A383959 The number of prime powers p^e having the property that e is a unitary divisor of the p-adic valuation of n.
%C A383959 First differs from A238949 at n = 64.
%C A383959 First differs from A383960 at n = 256.
%C A383959 Also, the number of prime powers p^e having the property that e is a squarefree divisor of the p-adic valuation of n.
%H A383959 Amiram Eldar, <a href="/A383959/b383959.txt">Table of n, a(n) for n = 1..10000</a>
%F A383959 Additive with a(p^e) = A034444(e) = 2^A001221(e).
%F A383959 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)*A034444(e)/p^e = 0.92341081050532387352... .
%t A383959 f[p_, e_] := 2^PrimeNu[e]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A383959 (PARI) a(n) = vecsum(apply(x -> 1 << omega(x), factor(n)[, 2]));
%Y A383959 Cf. A001221, A034444, A077761, A085548, A238949, A278908, A361255, A383863, A383960.
%K A383959 nonn,easy
%O A383959 1,4
%A A383959 _Amiram Eldar_, May 16 2025