A130491 - OEIS

A130491

a(n) = numerator of Sum_{k=1..n} k^mu(n+1-k), where mu(m) = A008683(m).

%I #13 Feb 10 2025 10:15:01

%S 1,3,9,35,91,179,117,1181,14113,1415,14839,35617,85271,53251,3503033,

%T 1879,12165719,106753,2870239,6436711,46663061,402271,850810423,

%U 60658043,1473361913,10236631,21081760033,39731443,2762347887557

%N a(n) = numerator of Sum_{k=1..n} k^mu(n+1-k), where mu(m) = A008683(m).

%C Denominator of Sum_{k=1..n} k^mu(n+1-k) is A130492(n).

%p A130491 := proc(n) numer(add(k^numtheory[mobius](n+1-k),k=1..n)) ; end: seq(A130491(n),n=1..40) ; # _R. J. Mathar_, Oct 16 2007

%t Table[Numerator[Sum[k^MoebiusMu[n+1-k],{k,n}]],{n,29}] (* _James C. McMahon_, Feb 09 2025 *)

%o (PARI) a(n) = numerator(sum(k=1, n, k^moebius(n+1-k))); \\ _Michel Marcus_, Feb 09 2025

%Y Cf. A130492, A080306, A080326.

%K frac,nonn

%O 1,2

%A _Leroy Quet_, May 29 2007

%E More terms from _R. J. Mathar_, Oct 16 2007