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A300244 Difference between A005187 and its Möbius transform (A297111). 7
0, 1, 1, 3, 1, 6, 1, 7, 4, 10, 1, 14, 1, 13, 11, 15, 1, 22, 1, 22, 14, 21, 1, 30, 8, 25, 16, 29, 1, 40, 1, 31, 22, 34, 18, 46, 1, 37, 26, 46, 1, 57, 1, 45, 38, 44, 1, 62, 11, 57, 35, 53, 1, 68, 26, 61, 38, 56, 1, 84, 1, 59, 51, 63, 30, 90, 1, 70, 45, 89, 1, 94, 1, 73, 65, 77, 29, 104, 1, 94, 50, 81, 1, 117, 39, 84, 57, 93, 1, 128, 33, 92, 60, 91, 42 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

FORMULA

a(n) = A005187(n) - A297111(n).

a(n) = -Sum_{d|n, d<n} A008683(n/d)*A005187(d).

MATHEMATICA

Table[IntegerExponent[(2 n)!, 2] - DivisorSum[n, IntegerExponent[(2 #)!, 2] MoebiusMu[n/#] &], {n, 95}] (* or *)

Fold[Function[{a, n}, Append[a, {Abs@ Total@ Map[MoebiusMu[n/#] a[[#, -1]] &, Most@ Divisors@ n], IntegerExponent[(2 n)!, 2]}]], {{0, 1}}, Range[2, 95]][[All, 1]] (* Michael De Vlieger, Mar 10 2018 *)

PROG

(PARI)

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

A300244(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A005187(d));

CROSSREFS

Cf. A005187, A008683, A297111, A297114, A297117.

Sequence in context: A324535 A318501 A318325 * A168111 A309491 A109646

Adjacent sequences:  A300241 A300242 A300243 * A300245 A300246 A300247

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 10 2018

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)