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A322671 a(n) = Sum_{d|n} (pod(d)/d), where pod(k) is the product of the divisors of k (A007955). 2
1, 2, 2, 4, 2, 9, 2, 12, 5, 13, 2, 155, 2, 17, 18, 76, 2, 336, 2, 415, 24, 25, 2, 13987, 7, 29, 32, 803, 2, 27035, 2, 1100, 36, 37, 38, 280418, 2, 41, 42, 64423, 2, 74133, 2, 1963, 2046, 49, 2, 5322467, 9, 2518, 54, 2735, 2, 157827, 58, 176427, 60, 61, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = n for n = 1, 2 and 4.

a(n) = n + (tau(n) - 1) = n + 3 for squarefree semiprimes (A006881).

a(n) = 2 if n is prime. - Robert Israel, Dec 23 2018

EXAMPLE

For n = 6; a(6) = pod(1)/1 + pod(2)/2 + pod(3)/3 + pod(6)/6 = 1/1 + 2/2 + 3/3 + 36/6 = 9.

MAPLE

pod:= proc(n) convert(numtheory:-divisors(n), `*`) end proc:

f:= proc(n) local d; add(pod(d)/d, d = numtheory:-divisors(n)) end proc:

map(f, [$1..100]); # Robert Israel, Dec 23 2018

MATHEMATICA

Array[Sum[Apply[Times, Divisors@ d]/d, {d, Divisors@ #}] &, 59] (* Michael De Vlieger, Jan 19 2019 *)

PROG

(MAGMA) [&+[&*[c: c in Divisors(d)] / d: d in Divisors(n)]: n in [1..100]]

(PARI) a(n) = sumdiv(n, d, vecprod(divisors(d))/d); \\ Michel Marcus, Dec 23 2018

CROSSREFS

Cf. A007955, A322672.

Sequence in context: A173300 A181236 A280684 * A087909 A076078 A292786

Adjacent sequences:  A322667 A322668 A322669 * A322672 A322673 A322674

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Dec 23 2018

STATUS

approved

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Last modified May 26 03:51 EDT 2019. Contains 323579 sequences. (Running on oeis4.)