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A046985 Multiply perfect numbers whose average divisor is an integer and divides the number itself. 9
1, 6, 672, 30240, 32760, 23569920, 45532800, 14182439040, 51001180160, 153003540480, 403031236608, 13661860101120, 154345556085770649600, 9186050031556349952000, 143573364313605309726720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

sigma_0(n) is the number of divisors of n (A000005).

sigma_1(n) is the sum of the divisors of n [same as sigma(n)] (A000203).

LINKS

Table of n, a(n) for n=1..15.

FORMULA

a=s1/s0, b=(k*s0)/s1 and c=s1/k, where s1=sigma_1(k), s0=sigma_0(k), the sum and number of divisors of k; a, b, c are integers.

EXAMPLE

x=45532800, sigma_0=384, sigma_1=182131200. The three quotients are as follows: a=474300, b=96 and c=4.

PROG

(PARI) isok(n) = s1 = sigma(n); s0 = numdiv(n); !(s1 % n) && !(s1 % s0) && !((n*s0) % s1); \\ Michel Marcus, Dec 10 2013

CROSSREFS

Intersection of A003601, A007691 and A001599. Cf. A046986, A046987.

Sequence in context: A269842 A333639 A331724 * A159371 A159620 A125535

Adjacent sequences:  A046982 A046983 A046984 * A046986 A046987 A046988

KEYWORD

nonn

AUTHOR

Labos Elemer

EXTENSIONS

a(10)-a(15) from Donovan Johnson, Nov 30 2008

STATUS

approved

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Last modified October 5 23:01 EDT 2022. Contains 357261 sequences. (Running on oeis4.)