A300244 Difference between A005187 and its Möbius transform (A297111).

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

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: A318501 A318325 A378182 * A336646 A336647 A336645

Adjacent sequences: A300241 A300242 A300243 * A300245 A300246 A300247

Keyword

nonn

Author

Antti Karttunen, Mar 10 2018

Status

approved