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

0,1

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

Samuel Herts, Table of n, a(n) for n = 0..1650

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

Cf. A007814, A008892.

Sequence in context: A228754 A171830 A071506 * A125920 A176360 A185068

Adjacent sequences: A372642 A372643 A372644 * A372646 A372647 A372648

Keyword

nonn

Author

Samuel Herts, May 08 2024

Status

approved