

A255245


Numbers that divide the average of the squares of their aliquot parts.


2



10, 65, 140, 420, 2100, 2210, 20737, 32045, 200725, 207370, 1204350, 1347905, 1762645, 16502850, 31427800, 37741340, 107671200, 130643100, 200728169, 239719720, 357491225, 417225900, 430085380, 766750575, 1088692500, 1132409168, 1328204850, 1788379460
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OFFSET

1,1


COMMENTS

Ratio: 1, 1, 5, 10, 78, 1, 109, 565,...
If the ratio is equal to 1 we have 10, 65, 20737 (A140362).


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..59 (terms < 10^11)


EXAMPLE

Aliquot parts of 10 are 1, 2, 5. The average of their squares is (1^2 + 2^2 + 5^2) / 3 = (1 + 4 + 25) / 3 = 30 / 3 = 10 and 10 / 10 = 1.


MAPLE

with(numtheory); P:=proc(q) local a, b, k, n;
for n from 2 to q do a:=sort([op(divisors(n))]);
b:=add(a[k]^2, k=1..nops(a)1)/(nops(a)1);
if type(b/n, integer) then lprint(n);
fi; od; end: P(10^6);


MATHEMATICA

Select[Range[10^6], Mod[Mean[Most[Divisors[#]^2]], #]==0&] (* Ivan N. Ianakiev, Mar 03 2015 *)


PROG

(PARI) isok(n) = (q=(sumdiv(n, d, (d!=n)*d^2)/(numdiv(n)1))) && (type(q)=="t_INT") && ((q % n) == 0); \\ Michel Marcus, Feb 20 2015
(Python)
from __future__ import division
from sympy import factorint
A255245_list = []
for n in range(2, 10**9):
....s0 = s2 = 1
....for p, e in factorint(n).items():
........s0 *= e+1
........s2 *= (p**(2*(e+1))1)//(p**21)
....q, r = divmod(s2n**2, s01)
....if not (r or q % n):
........A255245_list.append(n) # Chai Wah Wu, Mar 08 2015


CROSSREFS

Cf. A001065, A255244.
Sequence in context: A033908 A233246 A229996 * A210369 A058920 A263472
Adjacent sequences: A255242 A255243 A255244 * A255246 A255247 A255248


KEYWORD

nonn


AUTHOR

Paolo P. Lava, Feb 20 2015


EXTENSIONS

More terms from Michel Marcus, Feb 20 2015
a(17)a(24) from Chai Wah Wu, Mar 08 2015
a(25)a(28) from Giovanni Resta, May 30 2016


STATUS

approved



