A324397 a(1) = 0; for n > 1, a(n) = A297114(A156552(n)).

0, 0, 0, 0, 0, 2, 0, 3, -2, 3, 0, 7, 0, 14, -2, 0, 0, 9, 0, 15, -6, 9, 0, 18, -4, 33, -2, 14, 0, 4, 0, 25, -2, 42, -4, 7, 0, 254, -26, 9, 0, 33, 0, 63, -2, 140, 0, 41, -8, 14, -34, 127, 0, 24, -12, 66, -90, 579, 0, 38, 0, 684, -2, 6, -4, 21, 0, 175, -2, 37, 0, 24, 0, 3587, -2, 304, -8, 85, 0, 73, -14, 2733, 0, 6, -52, 8707, -378, 11, 0, 3

Offset: 1

Author

Antti Karttunen, Mar 05 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4137

Crossrefs

Cf. A000203, A005187, A156552, A297114, A323243, A323244, A324103, A323247, A323248, A324396, A324398, A324542.

Programs

Mathematica

Array[If[# == 1, 0, Function[n, DivisorSum[n, MoebiusMu[n/#] (2 # - DigitCount[2 #, 2, 1] - DivisorSigma[1, #]) &]]@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]]] &, 90] (* Michael De Vlieger, Mar 11 2019 *)

PARI

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
\\ Slow: A297114(n) = sumdiv(n,d,moebius(n/d)*(A005187(d)-sigma(d)));
A297111(n) = sumdiv(n,d,moebius(n/d)*A005187(d));
A297114(n) = (A297111(n) - n);
A324397(n) = if(1==n,0,A297114(A156552(n)));

Formula

a(1) = 0; for n > 1, a(n) = A297114(A156552(n)).

For all n >= 1, a(2n-1) = A324103(2n-1).