A294649 a(n) = numerator(A206369(n))/n.

1, 1, 2, 3, 4, 1, 6, 5, 7, 2, 10, 1, 12, 3, 8, 11, 16, 7, 18, 3, 4, 5, 22, 5, 21, 6, 20, 9, 28, 4, 30, 21, 20, 8, 24, 7, 36, 9, 8, 1, 40, 2, 42, 15, 28, 11, 46, 11, 43, 21, 32, 9, 52, 10, 8, 15, 12, 14, 58, 2, 60, 15, 2, 43, 48, 10, 66, 12, 44, 12, 70, 35, 72, 18, 14

Offset

1,3

Comments

a(n) = 1 for n in A127724.

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

László Tóth, A survey of the alternating sum-of-divisors function, arXiv:1111.4842 [math.NT], 2011-2014.

Mathematica

(* b = A209369 *) b[n_] := n*DivisorSum[n, LiouvilleLambda[#]/# &];
a[n_] := Numerator[b[n]/n];
Array[a, 100] (* Jean-François Alcover, Dec 04 2017 *)

Prog

(PARI) rhope(p, e) = my(s=1); for(i=1, e, s=s*p + (-1)^i); s;
rho(n) = my(f=factor(n)); prod(i=1, #f~, rhope(f[i, 1], f[i, 2]));
a(n) = numerator(rho(n)/n);

Crossrefs

Cf. A127724 (k-imperfect), A206369, A294650 (denominator).

A225679 is a subsequence (on squarefree indices). - Michel Marcus, Dec 22 2017

Sequence in context: A330342 A065338 A316272 * A350778 A001438 A342410

Adjacent sequences: A294646 A294647 A294648 * A294650 A294651 A294652

Keyword

nonn,frac

Author

Michel Marcus, Nov 06 2017

Status

approved