A300723 Möbius-transform of A005187(A053645(n)).

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

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: A347679 A028586 A253179 * A263788 A355335 A292144

Adjacent sequences: A300720 A300721 A300722 * A300724 A300725 A300726

Keyword

sign

Author

Antti Karttunen, Mar 12 2018

Status

approved