A380118 a(n) = Sum_{k=1..n} (A014963(k) - A061397(k)).

1, 1, 1, 3, 3, 4, 4, 6, 9, 10, 10, 11, 11, 12, 13, 15, 15, 16, 16, 17, 18, 19, 19, 20, 25, 26, 29, 30, 30, 31, 31, 33, 34, 35, 36, 37, 37, 38, 39, 40, 40, 41, 41, 42, 43, 44, 44, 45, 52, 53, 54, 55, 55, 56, 57, 58, 59, 60, 60, 61, 61, 62, 63, 65, 66, 67, 67, 68, 69, 70

Offset: 1

Author

Peter Luschny, Jan 30 2025

Keywords

• nonn

Crossrefs

Cf. A014963, A061397, A048671, A010051, A182936, A034387, A072107, A380117.

Programs

Maple

pSum := L -> ListTools:-PartialSums(L): h := n -> n/A048671(n) - n*A010051(n):
aList := upto -> pSum([seq(h(k), k = 1..upto)]): aList(70);

Mathematica

Accumulate[Table[Exp[MangoldtLambda[n]] - If[PrimeQ[n], n, 0] , {n, 1, 70}]]

Formula

a(n) = A072107(n) - A034387(n). - Amiram Eldar, Jan 30 2025