A286357 One more than the exponent of the highest power of 2 dividing sigma(n): a(n) = A001511(A000203(n)).

1, 1, 3, 1, 2, 3, 4, 1, 1, 2, 3, 3, 2, 4, 4, 1, 2, 1, 3, 2, 6, 3, 4, 3, 1, 2, 4, 4, 2, 4, 6, 1, 5, 2, 5, 1, 2, 3, 4, 2, 2, 6, 3, 3, 2, 4, 5, 3, 1, 1, 4, 2, 2, 4, 4, 4, 5, 2, 3, 4, 2, 6, 4, 1, 3, 5, 3, 2, 6, 5, 4, 1, 2, 2, 3, 3, 6, 4, 5, 2, 1, 2, 3, 6, 3, 3, 4, 3, 2, 2, 5, 4, 8, 5, 4, 3, 2, 1, 3, 1, 2, 4, 4, 2, 7, 2, 3, 4, 2, 4, 4, 4, 2, 5, 5, 2, 2, 3, 5, 4

Offset: 1

Author

Antti Karttunen, May 10 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A000523, A001511, A053866, A070939, A082903, A161942, A286358.

Programs

Mathematica

Table[IntegerExponent[DivisorSigma[1,n],2]+1,{n,120}] (* Harvey P. Dale, Sep 04 2023 *)

PARI

A001511(n) = (1+valuation(n,2));
A286357(n) = A001511(sigma(n));
for(n=1, 10000, write("b286357.txt", n, " ", A286357(n)));

Python

from sympy import divisor_sigma as D
def a001511(n): return bin(n)[2:][::-1].index("1") + 1
def a(n): return a001511(D(n)) # Indranil Ghosh, May 12 2017

Python

from sympy import divisor_sigma
def A286357(n): return ((m:=int(divisor_sigma(n)))&-m).bit_length() # Chai Wah Wu, Jul 10 2022

Scheme

(define (A286357 n) (A001511 (A000203 n)))
(define (A286357 n) (A070939 (/ (A000203 n) (A161942 n))))

Formula

a(n) = A001511(A000203(n)).

a(n) = 1 + A000523(A000203(n)/A161942(n)). [See also A082903.]

a(n) = 1 iff A053866(n) = 1.