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 A329638 Sum of A329644(d) for all such divisors d of n for which that value is positive. Here A329644 is the Möbius transform of A323244, the deficiency of A156552(n). 7
 0, 1, 1, 2, 1, 4, 1, 6, 1, 5, 1, 10, 1, 16, 2, 6, 1, 13, 1, 18, 2, 18, 1, 22, 1, 46, 5, 22, 1, 10, 1, 30, 14, 82, 2, 19, 1, 256, 2, 22, 1, 41, 1, 66, 9, 226, 1, 46, 1, 24, 8, 130, 1, 29, 2, 70, 2, 748, 1, 42, 1, 1362, 22, 30, 10, 42, 1, 214, 254, 44, 1, 43, 1, 3838, 15, 406, 2, 120, 1, 78, 5, 5458, 1, 52, 2, 12250, 2, 70, 1, 26, 2, 934 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552) Index entries for sequences related to binary expansion of n Index entries for sequences computed from indices in prime factorization Index entries for sequences related to sigma(n) FORMULA a(n) = Sum_{d|n} [A329644(d) > 0] * A329644(d), where [ ] is Iverson bracket. a(n) = A323244(n) + A329639(n). PROG (PARI) A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552 A323243(n) = if(1==n, 0, sigma(A156552(n))); A324543(n) = sumdiv(n, d, moebius(n/d)*A323243(d)); A297113(n) = if(1==n, 0, (primepi(vecmax(factor(n)[, 1])) + (bigomega(n)-omega(n)))); A329644(n) = if(1==n, 0, 2^A297113(n) - A324543(n)); A329638(n) = sumdiv(n, d, if((d=A329644(d))>0, d, 0)); CROSSREFS Cf. A156552, A323243, A323244, A329639, A329641, A329644. Cf. also A318878. Sequence in context: A340081 A346467 A329641 * A322036 A318441 A161510 Adjacent sequences: A329635 A329636 A329637 * A329639 A329640 A329641 KEYWORD nonn AUTHOR Antti Karttunen, Nov 21 2019 STATUS approved

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Last modified April 20 22:14 EDT 2024. Contains 371848 sequences. (Running on oeis4.)