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A300723 Möbius-transform of A005187(A053645(n)). 4
0, 0, 1, 0, 1, 2, 4, 0, 0, 2, 4, 4, 8, 6, 9, 0, 1, 0, 4, 4, 3, 6, 11, 8, 15, 10, 18, 12, 23, 10, 26, 0, -4, 2, -1, 0, 8, 6, 2, 8, 16, 2, 19, 12, 12, 14, 26, 16, 28, 16, 33, 20, 39, 20, 37, 24, 42, 26, 50, 20, 54, 30, 49, 0, -8, -6, 4, 4, -4, -2, 11, 0, 16, 10, -7, 12, 15, 2, 26, 16, 13, 18, 35, 4, 37, 22, 18, 24, 47, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = Sum_{d|n} A008683(n/d)*A005187(A053645(d)).

a(1) = 0; for n > 1, a(n) = A297111(n) - 2*A300724(n).

MATHEMATICA

With[{s = Array[2 # - DigitCount[2 #, 2, 1] &[# - 2^Floor@ Log2@ #] &, 90]}, Table[DivisorSum[n, MoebiusMu[n/#] s[[#]] &], {n, Length@ s}]] (* Michael De Vlieger, Mar 13 2018 *)

PROG

(PARI)

A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };

A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644

A053645(n) = (n-A053644(n));

A300723(n) = sumdiv(n, d, moebius(n/d)*A005187(A053645(d)));

CROSSREFS

Cf. A005187, A008683, A053645, A297111, A300724, A300725.

Sequence in context: A126732 A028586 A253179 * A263788 A292144 A300324

Adjacent sequences:  A300720 A300721 A300722 * A300724 A300725 A300726

KEYWORD

sign

AUTHOR

Antti Karttunen, Mar 12 2018

STATUS

approved

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Last modified February 20 22:51 EST 2019. Contains 320362 sequences. (Running on oeis4.)