A346111 a(n) = Sum_{primes p <=n} sigma(floor(n/p)).

0, 1, 2, 4, 5, 8, 9, 12, 13, 14, 15, 24, 25, 23, 23, 30, 31, 35, 36, 44, 41, 37, 38, 61, 60, 48, 46, 59, 60, 71, 72, 79, 74, 63, 58, 95, 96, 79, 66, 95, 96, 102, 103, 110, 108, 98, 99, 142, 138, 114, 102, 116, 117, 136, 129, 152, 134, 110, 111, 191, 192, 154, 142

Offset: 1

Author

Michel Marcus, Jul 05 2021

Keywords

• nonn

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A013939 (with k instead of sigma(k)), A344672 (with phi instead).

Programs

Mathematica

a[n_] := Plus @@ DivisorSigma[1, Floor[n/Select[Range[n], PrimeQ]]]; Array[a, 100] (* Amiram Eldar, Jul 05 2021 *)

PARI

a(n) = my(s=0); forprime(p=2, n, s+=sigma(n\p)); s;