A372645 - OEIS

%I #50 Sep 07 2024 08:54:44

%S 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 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 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 a(n) is the 2-adic valuation of the n-th term of the aliquot sequence of 276.

%C a(n) is the exponent of prime 2 in the prime factorization of A008892(n).

%C 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 Amiram Eldar, <a href="/A372645/b372645.txt">Table of n, a(n) for n = 0..2146</a> (terms 0..1650 from Samuel Herts)

%H Carl Pomerance, <a href="https://mathtube.org/lecture/video/aliquot-sequences">Aliquot Sequences</a>, The Unsolved Problems Conference, 2020.

%F a(n) = A007814(A008892(n)).

%e 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 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 (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 Cf. A007814, A008892.

%K nonn

%O 0,1

%A _Samuel Herts_, May 08 2024