A323706 a(n) = numerator of Sum_{d|n} tau(d)/pod(d) where tau(k) = the number of the divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).

1, 2, 5, 19, 7, 25, 9, 39, 16, 61, 13, 101, 15, 113, 469, 2501, 19, 2809, 21, 11263, 865, 265, 25, 133489, 178, 365, 1300, 29431, 31, 327601, 33, 40019, 2017, 613, 2069, 3659761, 39, 761, 2773, 921041, 43, 1203049, 45, 109255, 66692, 1105, 49, 410700293, 444

Offset

1,2

Comments

Sum_{d|n} tau(d)/pod(d) > 1 for all n > 1.

Links

Table of n, a(n) for n=1..49.

Formula

a(p) = p + 2 for prime p > 2.

Example

For n=4; Sum_{d|4} tau(d)/pod(d) = tau(1)/pod(1) + tau(2)/pod(2) + tau(4)/pod(4) = 1/1 + 2/2 + 3/8 = 19/8; a(4) = 19.

Prog

(Magma) [Numerator(&+[NumberOfDivisors(d) / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = numerator(sumdiv(n, d, numdiv(d)/vecprod(divisors(d)))); \\ Michel Marcus, Jan 25 2019

Crossrefs

Cf. A000005, A007955, A323707 (denominator).

Sequence in context: A289126 A062097 A356366 * A125765 A068873 A035091

Adjacent sequences: A323703 A323704 A323705 * A323707 A323708 A323709

Keyword

nonn,frac

Author

Jaroslav Krizek, Jan 24 2019

Status

approved