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A372645
a(n) is the 2-adic valuation of the n-th term of the aliquot sequence of 276.
1
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, 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, 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
OFFSET
0,1
COMMENTS
a(n) is the exponent of prime 2 in the prime factorization of A008892(n).
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.
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..2146 (terms 0..1650 from Samuel Herts)
Carl Pomerance, Aliquot Sequences, The Unsolved Problems Conference, 2020.
FORMULA
a(n) = A007814(A008892(n)).
EXAMPLE
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.
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.
PROG
(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
CROSSREFS
Sequence in context: A228754 A171830 A071506 * A125920 A176360 A185068
KEYWORD
nonn
AUTHOR
Samuel Herts, May 08 2024
STATUS
approved