A351367 a(n) = Sum_{p|n, p prime} p^nextprime(p), where nextprime(n) is the smallest prime > n.

0, 8, 243, 8, 78125, 251, 1977326743, 8, 243, 78133, 34522712143931, 251, 8650415919381337933, 1977326751, 78368, 8, 239072435685151324847153, 251, 257829627945307727248226067259, 78133, 1977326986, 34522712143939, 3091058643093537522799545838540043339063, 251, 78125

Offset

1,2

Comments

Inverse Möbius transform of n^nextprime(n) * c(n), where c(n) is the characteristic function of primes (A010051). - Wesley Ivan Hurt, Apr 01 2025

Links

Table of n, a(n) for n=1..25.

Formula

a(n) = Sum_{d|n} d^nextprime(d) * c(d), where c = A010051. - Wesley Ivan Hurt, Apr 01 2025

Example

a(6) = 251; a(6) = Sum_{p|6} p^nextprime(p) = 2^nextprime(2) + 3^nextprime(3) = 2^3 + 3^5 = 251.

Crossrefs

Cf. A010051, A151800 (nextprime v.2), A345280, A345281.

Sequence in context: A158263 A367629 A221417 * A351370 A272236 A272239

Adjacent sequences: A351364 A351365 A351366 * A351368 A351369 A351370

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 08 2022

Status

approved