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URL: https://oeis.org/A229095

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A229095
Numbers k such that Sum_{i=1..k} i^tau(i) == 0 (mod k), where tau(i) = A000005(i), the number of divisors of i.
6
1, 8, 9, 67, 72, 467, 801, 1071, 5141, 7193, 25688, 68488, 97768, 111816, 381061, 7829505, 17079937, 25615576, 44582211, 91110856, 639359784, 3492789629
OFFSET
1,2
EXAMPLE
1^tau(1) + 2^tau(2) + ... + 8^tau(8) + 9^tau(9) = 1^1 + 2^2 + 3^2 + 4^3 + 5^2 + 6^4 + 7^2 + 8^4 + 9^3 = 6273 and 6273 / 9 = 697.
MAPLE
with(numtheory); P:=proc(q) local n, t; t:=0;
for n from 1 to q do t:=t+n^tau(n); if t mod n=0 then print(n);
fi; od; end: P(10^6);
PROG
(PARI) list(lim) = {my(s = 0, f); for(k = 1, lim, s += k^numdiv(k); if(!(s % k), print1(k, ", "))); } \\ Amiram Eldar, Dec 29 2024
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Sep 13 2013
EXTENSIONS
a(16)-a(18) from Jinyuan Wang, Feb 18 2021
a(19)-a(22) from Amiram Eldar, Dec 29 2024
STATUS
approved