A175548 Binary weight of sigma(n).

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

Offset: 1

Author

Vladimir Shevelev, Dec 03 2010

Keywords

• nonn
• base

Comments

The sequence is considered in connection with A175522, A175524, A175526.

a(n)=1 if n is in A046528. - Robert Israel, Nov 07 2017

Examples

			a(4) = 3 because the divisors of 4 add up to 7, a number which in binary is written as 3 ones.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A000203, A000120, A046528, A175522, A175524, A175526.

Programs

Maple

seq(convert(convert(numtheory:-sigma(n),base,2),`+`),n=1..100); # Robert Israel, Nov 07 2017

Mathematica

Table[Plus@@IntegerDigits[DivisorSigma[1, n], 2], {n, 80}] (* Alonso del Arte, Dec 03 2010 *)

PARI

a(n) = hammingweight(sigma(n)); \\ Michel Marcus, Feb 08 2016

Formula

a(n) = A000120(A000203(n)).

Extensions

More terms from Antti Karttunen, Nov 07 2017