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 A344537 #12 Dec 23 2024 21:51:00
%S A344537 0,1,2,4,8,3,64,5,16,9,1024,6,32768,65,10,32,2097152,17,268435456,12,
%T A344537 66,1025,68719476736,7,128,32769,18,68,35184372088832,11,
%U A344537 36028797018963968,33,1026,2097153,72,20,73786976294838206464,268435457,32770,13
%N A344537 Inverse permutation to A344535.
%C A344537 This sequence is additive.
%C A344537 This sequence establishes a bijection from A225547 to A261195.
%H A344537 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A344537 a(prime(n)) = A006125(n+1) for any n >= 0.
%F A344537 a(2^2^n) = A036442(n).
%F A344537 A000120(a(n)) = A064547(n).
%F A344537 a(A225546(n)) = A344536(n).
%F A344537 a(n) = A344536(n) iff n belongs to A225547.
%e A344537 A344535(42) = 240, so a(240) = 42.
%o A344537 (PARI) a(n) = { my (f=factor(n), v=0); for (k=1, #f~, my (x=primepi(f[k, 1])-1, yy=f[k, 2], y); while (yy, yy-=2^y=valuation(yy, 2); v+=2^(y + (x+y)*(x+y+1)/2))); v }
%Y A344537 Cf. A000120, A006125, A036442, A064547, A225546, A225547, A261195, A344535, A344536.
%K A344537 nonn,base
%O A344537 1,3
%A A344537 _Rémy Sigrist_, May 23 2021