A343274 a(n) = Sum_{d|n} d^d * sopf(d).

0, 8, 81, 520, 15625, 233369, 5764801, 33554952, 1162261548, 70000015633, 3138428376721, 44580502475161, 3937376385699289, 100008061435786953, 3503151123046890706, 36893488147452658184, 14063084452067724991009, 196732040376483850371956, 37589973457545958193355601

Offset

1,2

Comments

If p is prime, a(p) = Sum_{d|p} d^d * sopf(d) = 1^1*0 + p^p*p = p^(p+1).

Links

Table of n, a(n) for n=1..19.

Example

a(4) = Sum_{d|4} d^d * sopf(d) = 1^1*sopf(1) + 2^2*sopf(2) + 4^4*sopf(4) = 0 + 8 + 512 = 520.

Mathematica

Table[Sum[i^i*Sum[k (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[i/k] + Floor[i/k]), {k, i}] (1 - Ceiling[n/i] + Floor[n/i]) , {i, n}], {n, 20}]

Crossrefs

Cf. A008472 (sopf).

Sequence in context: A303515 A027768 A236749 * A240480 A274752 A240632

Adjacent sequences: A343271 A343272 A343273 * A343275 A343276 A343277

Keyword

nonn

Author

Wesley Ivan Hurt, May 24 2021

Status

approved