A372645 a(n) is the 2-adic valuation of the n-th term of the aliquot sequence of 276.

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

Author

Samuel Herts, May 08 2024

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

Cf. A007814, A008892.

Programs

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

Formula

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