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 A372645 #50 Sep 07 2024 08:54:44 %S A372645 2,2,3,4,4,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, %T A372645 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, %U A372645 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2 %N A372645 a(n) is the 2-adic valuation of the n-th term of the aliquot sequence of 276. %C A372645 a(n) is the exponent of prime 2 in the prime factorization of A008892(n). %C A372645 An empirical observation would suggest that this sequence may be a(n) = 1 for n >= 793 since the likelihood of a parity switch becomes exponentially small. %H A372645 Amiram Eldar, <a href="/A372645/b372645.txt">Table of n, a(n) for n = 0..2146</a> (terms 0..1650 from Samuel Herts) %H A372645 Carl Pomerance, <a href="https://mathtube.org/lecture/video/aliquot-sequences">Aliquot Sequences</a>, The Unsolved Problems Conference, 2020. %F A372645 a(n) = A007814(A008892(n)). %e A372645 For n=4, the term in the aliquot sequence of 276 after 4 steps is A008892(4) = 1872 = 2^4 * 3^2 * 13 and the exponent of 2 there is a(4) = 4. %e A372645 For n=30, the term in the aliquot sequence of 276 after 30 steps is A008892(30) = 23117724 = 2^2 * 3^4 * 7 * 10193 and the exponent of 2 there is a(30) = 2. %o A372645 (PARI) lista(nn) = my(v = vector(nn)); v[1] = 276; for (n=2, nn, v[n] = sigma(v[n-1]) - v[n-1];); apply(x->valuation(x, 2), v); \\ _Michel Marcus_, May 14 2024 %Y A372645 Cf. A007814, A008892. %K A372645 nonn %O A372645 0,1 %A A372645 _Samuel Herts_, May 08 2024