A345311 - OEIS

A345311

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

0, 4, 27, 4, 3125, 793, 823543, 16, 27, 9766649, 285311670611, 531505, 302875106592253, 678223089233, 30531927032, 256, 827240261886336764177, 262873, 1978419655660313589123979, 95367431641649, 558545874543637210, 81402749386839765307625, 20880467999847912034355032910567

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..23.

Index entries for sequences related to lcm's

EXAMPLE

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

MATHEMATICA

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