A046985 Multiply perfect numbers whose average divisor is an integer and divides the number itself.

1, 6, 672, 30240, 32760, 23569920, 45532800, 14182439040, 51001180160, 153003540480, 403031236608, 13661860101120, 154345556085770649600, 9186050031556349952000, 143573364313605309726720

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