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

1,2

Comments

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

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

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A296525 A333766 A333226 * A038571 A008687 A290251

Adjacent sequences: A175545 A175546 A175547 * A175549 A175550 A175551

Keyword

nonn,base

Author

Vladimir Shevelev, Dec 03 2010

Extensions

More terms from Antti Karttunen, Nov 07 2017

Status

approved