login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 06:10 EDT 2019. Contains 328046 sequences. (Running on oeis4.)