A348976 Möbius transform of A129283, which is sum of n and its arithmetic derivative.

1, 2, 3, 5, 5, 5, 7, 12, 11, 9, 11, 12, 13, 13, 14, 28, 17, 17, 19, 22, 20, 21, 23, 28, 29, 25, 39, 32, 29, 22, 31, 64, 32, 33, 34, 40, 37, 37, 38, 52, 41, 32, 43, 52, 50, 45, 47, 64, 55, 49, 50, 62, 53, 57, 54, 76, 56, 57, 59, 52, 61, 61, 72, 144, 64, 52, 67, 82, 68, 58, 71, 92, 73, 73, 78, 92, 76, 62, 79, 120

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = Sum_{d|n} A008683(n/d) * A129283(d).

a(n) = A000010(n) + A300251(n).

Mathematica

f[p_, e_] := e/p; d[1] = 1; d[n_] := n*(1 + Plus @@ f @@@ FactorInteger[n]); a[n_] := DivisorSum[n, MoebiusMu[#]*d[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 13 2021 *)

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A129283(n) = (n+A003415(n));
A348976(n) = sumdiv(n, d, moebius(n/d)*A129283(d));

Crossrefs

Cf. A000010, A003415, A008683, A129283, A300251, A347084, A348970.

Sequence in context: A003660 A065688 A377543 * A169787 A165959 A347784

Adjacent sequences: A348973 A348974 A348975 * A348977 A348978 A348979

Keyword

nonn

Author

Antti Karttunen, Nov 09 2021

Status

approved