A309530 Number of power-of-two-divisors of sum of divisors of sum of divisors of powers of two: a(n) = A001511(A051027(A000079(n))).

1, 3, 4, 4, 6, 4, 8, 5, 5, 10, 5, 6, 14, 12, 12, 6, 18, 10, 20, 11, 9, 9, 6, 8, 8, 18, 6, 15, 7, 16, 32, 7, 11, 22, 17, 14, 7, 24, 22, 13, 5, 13, 11, 12, 20, 10, 7, 11, 9, 16, 33, 22, 6, 10, 15, 17, 28, 12, 6, 20, 62, 36, 12, 9, 24, 16, 5, 26, 12, 26, 10, 18, 6, 12, 16, 28, 19, 26

Offset

0,2

Links

Table of n, a(n) for n=0..77.

Juri-Stepan Gerasimov, x = A001511(A051027(A000079(x))), SeqFan list, Aug 19 2019.

Formula

a(n) = A001511(A051027(A000079(n))).

Example

a(0) = A001511(A051027(A000079(0))) = A001511(A051027(A000079(2^0))) = A001511(A051027(1)) = A001511(1) = 1.

Prog

(Magma) [Valuation(2*SumOfDivisors(SumOfDivisors(2^n)), 2): n in [0..89]];
(PARI) a(n) = valuation(2*sigma(sigma(2^n)), 2); \\ Michel Marcus, Aug 06 2019
(Python)
from sympy import divisor_sigma
def A309530(n): return ((m:=int(divisor_sigma((1<<n+1)-1)))&-m).bit_length() # Chai Wah Wu, Jul 13 2022

Crossrefs

Cf. A000043 (numbers m such that m - 1 divides a(m - 1) - 2), A000079, A001511, A051027, A090748.

Sequence in context: A222283 A336094 A182487 * A341933 A061117 A255171

Adjacent sequences: A309527 A309528 A309529 * A309531 A309532 A309533

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 06 2019

Status

approved