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

1,3

Links

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

Mathematica

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

Prog

(PARI) a(n) = my(s=0); forprime(p=2, n, s+=sigma(n\p)); s;
(Python)
from sympy import primepi, divisor_sigma
def A346111(n):
    c, j, j2 = 0, 1, 0
    while j <= n:
        k = n//j
        m = n//k
        c += (-j2+(j2:=primepi(m)))*divisor_sigma(k)
        j = m+1
    return c # Chai Wah Wu, Jun 24 2026

Crossrefs

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

Sequence in context: A334266 A211967 A099628 * A286805 A188072 A296058

Adjacent sequences: A346108 A346109 A346110 * A346112 A346113 A346114

Keyword

nonn

Author

Michel Marcus, Jul 05 2021

Status

approved