OFFSET
1,2
COMMENTS
a(12) > 200000. - Michel Marcus, Feb 25 2016
a(13) > 500000. - Harvey P. Dale, Dec 13 2018
a(14) > 3000000. - Jason Yuen, Feb 27 2024
EXAMPLE
tau(1)^1 + tau(2)^2 + ... + tau(45)^45 + tau(46)^46 = 1^1 + 2^2 + ... + 6^45 + 4^46 = 86543618042218910328339719795268200166 and 86543618042218910328339719795268200166 / 46 = 1881383000917802398442167821636265221.
MAPLE
with(numtheory); P:=proc(q) local n, t; t:=0;
for n from 1 to q do t:=t+tau(n)^n; if t mod n=0 then print(n);
fi; od; end: P(10^6);
MATHEMATICA
Module[{nn=30000, ac}, ac=Accumulate[Table[DivisorSigma[0, i]^i, {i, nn}]]; Select[ Thread[{ac, Range[nn]}], Divisible[#[[1]], #[[2]]]&]][[All, 2]](* Harvey P. Dale, Dec 13 2018 *)
PROG
(PARI) isok(n) = sum(i=1, n, Mod(numdiv(i), n)^i) == 0; \\ Michel Marcus, Feb 25 2016
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Sep 16 2013
EXTENSIONS
a(12) added by Harvey P. Dale, Dec 13 2018
a(13) added by Jason Yuen, Feb 27 2024
STATUS
approved