A329638 - OEIS

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).

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

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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