

A093653


Total number of 1's in binary expansion of all divisors of n.


12



1, 2, 3, 3, 3, 6, 4, 4, 5, 6, 4, 9, 4, 8, 9, 5, 3, 10, 4, 9, 9, 8, 5, 12, 6, 8, 9, 12, 5, 18, 6, 6, 8, 6, 9, 15, 4, 8, 10, 12, 4, 18, 5, 12, 15, 10, 6, 15, 7, 12, 9, 12, 5, 18, 11, 16, 10, 10, 6, 27, 6, 12, 17, 7, 8, 16, 4, 9, 10, 18, 5, 20, 4, 8, 16, 12, 11, 20, 6, 15, 12, 8, 5, 27, 9, 10, 12
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384 (first 500 terms from Jaroslav Krizek)
Maxwell Schneider, Robert Schneider, Digit sums and generating functions, arXiv:1807.06710 [math.NT], 2018. See (22) p. 6.
Index entries for sequences related to binary expansion of n


FORMULA

a(n) = Sum_{k = 0..n} if(mod(n, k) = 0, A000120(k), 0).  Paul Barry, Jan 14 2005
a(n) = A182627(n)  A226590(n).  Jaroslav Krizek, Sep 01 2013
a(n) = A292257(n) + A000120(n).  Antti Karttunen, Dec 14 2017


EXAMPLE

a(8) = 4 because the divisors of 8 are [1, 2, 4, 8] and in binary: 1, 10, 100, 1000, so four 1's.


MATHEMATICA

Table[Plus@@DigitCount[Divisors[n], 2, 1], {n, 75}] (* Alonso del Arte, Sep 01 2013 *)


PROG

(PARI) A093563(n) = sumdiv(n, d, hammingweight(d)); \\ Antti Karttunen, Dec 14 2017


CROSSREFS

Cf. A000120, A093687, A192895, A292257.
Cf. A226590 (number of 0's in binary expansion of all divisors of n).
Cf. A182627 (number of digits in binary expansion of all divisors of n).
Cf. A034690 (a decimal equivalent).
Sequence in context: A087688 A126854 A115206 * A205442 A049982 A245642
Adjacent sequences: A093650 A093651 A093652 * A093654 A093655 A093656


KEYWORD

base,easy,nonn


AUTHOR

Jason Earls, May 16 2004


STATUS

approved



