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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
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 (list; graph; refs; listen; history; text; internal format)
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: A197855 A289126 A062097 * A125765 A068873 A035091

Adjacent sequences:  A323703 A323704 A323705 * A323707 A323708 A323709

KEYWORD

nonn,frac

AUTHOR

Jaroslav Krizek, Jan 24 2019

STATUS

approved

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Last modified July 24 18:34 EDT 2021. Contains 346273 sequences. (Running on oeis4.)