A174933 a(n) = Sum_{d|n} A007955(d) * A000027(d) = Sum_{d|n} A007955(d) * (d), where A007955(m) = product of divisors of m.

1, 5, 10, 37, 26, 230, 50, 549, 253, 1030, 122, 20998, 170, 2798, 3410, 16933, 290, 105449, 362, 161062, 9320, 10774, 530, 7984134, 3151, 17750, 19936, 617486, 842, 24304630, 962, 1065509, 36068, 39598, 42950, 362923273, 1370, 55238, 59498, 102561574

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Example

For n = 4, A007955(n) = b(n): a(4) = b(1)*1 + b(2)*2 + b(4)*4 = 1*1 + 2*2 + 8*4 = 37.

Prog

(PARI) a(n)={sumdiv(n, d, vecprod(divisors(d))*d)} \\ Andrew Howroyd, Jan 05 2020
(Magma) [&+[&*Divisors(d)*d:d in Divisors(n)]:n in [1..40]]; // Marius A. Burtea, Jan 05 2020
(Python)
from math import isqrt
from sympy import divisor_count, divisors
def A174933(n): return sum(isqrt(d)**(c+2) if (c:=divisor_count(d)) & 1 else d**(c//2+1) for d in divisors(n, generator=True)) # Chai Wah Wu, Jun 25 2022

Crossrefs

Cf. A007955.

Sequence in context: A326232 A189732 A307607 * A270219 A270276 A271604

Adjacent sequences: A174930 A174931 A174932 * A174934 A174935 A174936

Keyword

nonn

Author

Jaroslav Krizek, Apr 02 2010

Extensions

Terms a(31) and beyond from Andrew Howroyd, Jan 05 2020

Status

approved