A120271 a(n) = numerator(Sum_{k=1..n} 1/(prime(k)-1)).

1, 3, 7, 23, 121, 21, 173, 1597, 17927, 127469, 129317, 43619, 44081, 44521, 1033223, 13538159, 395369371, 132680013, 400467919, 402757063, 1214947859, 1221110939, 50305908619, 50529880549, 101470376303, 509322834499, 8691337402883

Offset

1,2

Comments

a(n) is squarefree except for n = 5, 14, 49, ... where squared prime factors are 11, 211, 479, ...

a(n)/A128646(n) is the asymptotic mean over the positive integers of the number of prime divisors that are not greater than prime(n), counted with multiplicity (cf. A007814, A169611, A356006). - Amiram Eldar, Jul 23 2022

Links

Table of n, a(n) for n=1..27.

Eric Weisstein's World of Mathematics, Prime Sums.

Formula

a(n) = numerator(Sum_{k=1..n} 1/(prime(k)-1)).

a(n) = A078456(n) * A135212(n). - Alexander Adamchuk, Nov 23 2007

Mathematica

Numerator[Table[Sum[1/(Prime[i]-1), {i, 1, n}], {n, 1, 50}]]

Prog

(PARI) a(n) = numerator(sum(k=1, n, 1/(prime(k)-1))); \\ Michel Marcus, Oct 02 2016

Crossrefs

Cf. A128646 (denominators), A119686, A006093, A000040.

Cf. A135212, A078456.

Cf. A007814, A169611, A356006.

Sequence in context: A299404 A268140 A133788 * A145938 A329875 A048721

Adjacent sequences: A120268 A120269 A120270 * A120272 A120273 A120274

Keyword

frac,nonn

Author

Alexander Adamchuk, Jul 01 2006

Status

approved