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A255244
Numbers that divide the average of the sum of the squares of their divisors.
2
1, 65, 175, 1105, 5425, 20737, 32045, 70525, 103685, 171275, 200725, 207553, 352529, 372775, 1037765, 1198925, 1264957, 1347905, 1762645, 1824877, 2609425, 2698189, 3628975, 3928475, 4966975, 6324785, 6337175, 8646625, 8813225, 9124385, 10223341, 12774139, 13490945
OFFSET
1,2
LINKS
Chai Wah Wu and Giovanni Resta, Table of n, a(n) for n = 1..328 (terms < 10^12, first 82 terms from Chai Wah Wu)
EXAMPLE
Divisors of 65 are 1, 5, 13, 65. The average of the sum of their squares is (1^2 + 5^2 + 13^2 + 65^2) / 4 = (1 + 25 + 169 + 4225) / 4 = 4420 / 4 = 1105 and 1105 / 65 = 17.
MAPLE
with(numtheory); P:=proc(q) local a, b, k, n;
for n from 2 to q do a:=divisors(n);
b:=add(a[k]^2, k=1..nops(a))/nops(a);
if type(b/n, integer) then lprint(n);
fi; od; end: P(10^6);
MATHEMATICA
Select[Range[10^6], Mod[Mean[Divisors[#]^2], #]==0&] (* Ivan N. Ianakiev, Mar 03 2015 *)
PROG
(PARI) isok(n) = (q=sumdiv(n, d, d^2)/numdiv(n)) && (type(q)=="t_INT") && ((q % n) == 0); \\ Michel Marcus, Feb 20 2015
(Python)
from __future__ import division
from sympy import factorint
A255244_list = []
for n in range(1, 10**9):
....s0 = s2 = 1
....for p, e in factorint(n).items():
........s0 *= e+1
........s2 *= (p**(2*(e+1))-1)//(p**2-1)
....q, r = divmod(s2, s0)
....if not (r or q % n):
........A255244_list.append(n) # Chai Wah Wu, Mar 08 2015
CROSSREFS
Sequence in context: A044397 A044778 A054902 * A261989 A051968 A242318
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Feb 20 2015
EXTENSIONS
More terms from Michel Marcus, Feb 20 2015
a(31)-a(33) corrected by Chai Wah Wu, Mar 08 2015
STATUS
approved