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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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A000203, A255245.

Sequence in context: A044397 A044778 A054902 * A261989 A051968 A242318

Adjacent sequences:  A255241 A255242 A255243 * A255245 A255246 A255247

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

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)