|
|
A227008
|
|
Numbers k such that Sum_{j=1..k} (sigma(j) + phi(j) + tau(j)) == 0 (mod k).
|
|
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
|
|
|
LINKS
|
|
|
EXAMPLE
|
Sum_{j=1..399} sigma(j) = 130973;
Sum_{j=1..399} phi(j) = 48518;
Sum_{j=1..399} tau(j) = 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
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|