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 A382291 #11 Mar 21 2025 10:04:12 %S A382291 1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,1,1,2,1,1, %T A382291 1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,2,1,1,1,1, %U A382291 1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1 %N A382291 a(n) = A037445(n)/A034444(n). %C A382291 First differs from A368168 at n = 64, and from A359411, A367516 and A368979 at n = 128. %H A382291 Amiram Eldar, <a href="/A382291/b382291.txt">Table of n, a(n) for n = 1..10000</a> %F A382291 a(n) = 2^A382290(n). %F A382291 Multiplicative with a(p^e) = 2^(A000120(e)-1) = A048896(e-1) (= A243036(e) for e >= 2). %F A382291 a(n) >= 1, with equality if and only if n is in A138302. %F A382291 a(n) = 2 if and only if n is in A382292. %t A382291 f[p_, e_] := 2^(DigitCount[e, 2, 1] - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 105] %o A382291 (PARI) a(n) = vecprod(apply(x -> 1 << (hammingweight(x)-1), factor(n)[, 2])); %Y A382291 Cf. A000120, A034444, A037445, A138302, A243036, A382290, A382292. %Y A382291 Cf. A359411, A367516, A368168, A368979. %K A382291 nonn,easy,mult %O A382291 1,8 %A A382291 _Amiram Eldar_, Mar 21 2025