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A227008 Numbers n such that (sum_{k=1..n} sigma(k) + phi(k) + tau(k)) == 0 mod n. 0
1, 399, 872, 1214, 2090, 5200, 5588, 21208, 29152, 638049, 1627676, 151732410, 274845607, 3224070252, 54892040166, 69020111756, 175288968221 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(17) > 10^11. - Donovan Johnson, Jul 07 2013

a(18) > 5*10^11. - Giovanni Resta, Jul 11 2013

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

sum_{k=1..399} sigma(k) = 130973.

sum_{k=1..399} phi(k) = 48518.

sum_{k=1..399} tau(k) = 2453.

(130973 + 48518 + 2453) / 399 = 456.

MAPLE

with(numtheory); ListA227008:=proc(q, h) local a, n;  a:=0;

for n from 1 to q do  a:=a+sigma(n)+phi(n)+tau(n); if (a mod n)=0 then print(n); fi; od; end: ListA227008(10^9);

PROG

(PARI) s=0; for(n=1, 274845607, s=s+sigma(n)+eulerphi(n)+numdiv(n); if(s%n==0, print(n " " s))) /* Donovan Johnson, Jul 06 2013 */

CROSSREFS

Cf. A000005, A000010, A000203.

Sequence in context: A202158 A126231 A158317 * A253597 A006972 A216925

Adjacent sequences:  A227005 A227006 A227007 * A227009 A227010 A227011

KEYWORD

nonn,more

AUTHOR

Paolo P. Lava, Jun 27 2013

EXTENSIONS

a(11)-a(14) from Donovan Johnson, Jul 06 2013

a(15)-a(16) from Donovan Johnson, Jul 07 2013

a(17) from Giovanni Resta, Jul 11 2013

STATUS

approved

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Last modified April 26 08:35 EDT 2019. Contains 322472 sequences. (Running on oeis4.)