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A226563 Numbers n such that sum(d|n, sigma(d)^2) is a multiple of n. 4
1, 2, 10, 185, 370, 3145, 6290, 40885, 53465, 63750, 81770, 106930, 241400, 348750, 427720, 828750, 866200, 1207000, 1306875, 1635449, 2613750, 3138200, 3270898, 7149375, 8054345, 8177245, 14298750, 14725400, 15691000, 16108690, 16354490, 16989375, 30368120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..71 (terms < 2*10^9)

EXAMPLE

Divisors of 3145 are 1, 5, 17, 37, 85, 185, 629, 3145.

sigma(1) = 1, sigma(5) = 6, sigma(17) = 18, sigma(37) = 38, sigma(85) = 108, sigma(185) = 228, sigma(629) = 684, sigma(3145) = 4104.

(1^2 + 6^2 + 18^2 + 38^2 + 108^2 + 228^2 + 684^2 + 4104^2) / 3145 = 5525.

MAPLE

with(numtheory); ListA226563:=proc(q) local a, b, k, n;

for n from 1 to q do a:=[op(divisors(n))]; b:=add(sigma(a[k])^2, k=1..nops(a));

if type(b/n, integer) then print(n); fi; od; end: ListA226563(10^6);

CROSSREFS

Cf. A068978, A068986, A226564-A226566

Sequence in context: A086675 A319607 A057119 * A037267 A177399 A194971

Adjacent sequences:  A226560 A226561 A226562 * A226564 A226565 A226566

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Jun 11 2013

EXTENSIONS

a(14)-a(33) from Giovanni Resta, Jun 11 2013

STATUS

approved

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)