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 A324054 #22 Mar 10 2023 16:35:15
%S A324054 1,3,4,7,6,12,13,15,8,18,24,28,31,39,40,31,12,24,32,42,48,72,78,60,57,
%T A324054 93,124,91,156,120,121,63,14,36,48,56,72,96,104,90,96,144,192,168,248,
%U A324054 234,240,124,133,171,228,217,342,372,403,195,400,468,624,280,781,363,364,127,18,42,56,84,84,144,156,120,112,216,288,224
%N A324054 a(n) = A000203(A005940(1+n)).
%C A324054 As noted by _David A. Corneth_, the function f(n) = a(n-1) [that is, the offset-1 version of this sequence] seems to be "almost multiplicative". Sequence A324109 gives the positions n where f(n) satisfies the multiplicativity in a sense that f(n) = f(p(1)^e(1)) * ... * f(p(k)^e(k)), when n = p(1)^e(1) * ... * p(k)^e(k), and A324110 the positions where this does not hold.
%H A324054 Antti Karttunen, <a href="/A324054/b324054.txt">Table of n, a(n) for n = 0..8191</a>
%H A324054 Antti Karttunen, <a href="/A324054/a324054.txt">Data supplement: n, a(n) computed for n = 0..70327</a>
%H A324054 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324054 Michael De Vlieger, <a href="/A324054/a324054.png">Annotated fan-style binary tree diagram</a> showing 16 levels, where blue represents A336834(n) = 1 and yellow A336834(n) = 0. Labels are a(n) for the 8 smallest levels.
%F A324054 a(n) = A000203(A005940(1+n)).
%F A324054 a(n) = A324056(n) * A038712(1+n).
%t A324054 nn = 76; a[0] = 1; Do[Set[a[n], Prime[1 + DigitCount[n, 2, 0]]*a[n - 2^Floor@ Log2@ n]], {n, nn}]; Array[DivisorSigma[1, a[#]] &, nn, 0] (* _Michael De Vlieger_, Aug 03 2022 *)
%o A324054 (PARI)
%o A324054 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A324054 A324054(n) = sigma(A005940(1+n));
%o A324054 (PARI) A324054(n) = { my(p=2,mp=p*p,m=1); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, if(3==(n%4),mp *= p,m *= (mp-1)/(p-1))); n>>=1); (m); };
%o A324054 (Python)
%o A324054 from math import prod
%o A324054 from itertools import accumulate
%o A324054 from collections import Counter
%o A324054 from sympy import prime
%o A324054 def A324054(n): return prod(((p:=prime(len(a)+1))**(b+1)-1)//(p-1) for a, b in Counter(accumulate(bin(n)[2:].split('1')[:0:-1])).items()) # _Chai Wah Wu_, Mar 10 2023
%Y A324054 Cf. A000203, A005940, A038712, A324055, A324056, A324057, A324058, A324108, A324109, A324110, A324111, A324112, A356321.
%Y A324054 Cf. also A106737, A290077 (tau and phi similarly permuted).
%K A324054 nonn
%O A324054 0,2
%A A324054 _Antti Karttunen_, Feb 14 2019