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 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. 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

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