A345313 a(n) = Sum_{p|n, p prime} (n/p)^lcm(p,n/p).

0, 1, 1, 4, 1, 793, 1, 256, 27, 9766649, 1, 16823872, 1, 678223089233, 30531927032, 16777216, 1, 150094635297045777, 1, 1109511627776, 558545874543637210, 81402749386839765307625, 1, 4722366491785745661952, 3125, 91733330193268616658466724873, 387420489

Offset

1,4

Comments

a(p) = Sum_{p|p} (p/p)^lcm(p,p/p) = 1^p = 1 for primes p.

Links

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

Index entries for sequences related to lcm's

Example

a(10) = Sum_{p|10} (10/p)^lcm(p,10/p) = 5^lcm(2,5) + 2^lcm(5,2) = 5^10 + 2^ 10 = 9766649.

Mathematica

Table[Sum[(n/k)^LCM[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 30}]

Crossrefs

Sequence in context: A298939 A240098 A094337 * A038019 A164804 A036115

Adjacent sequences: A345310 A345311 A345312 * A345314 A345315 A345316

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 13 2021

Status

approved