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.

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

Links

Table of n, a(n) for n=1..22.

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

Cf. A000005, A227427, A227429, A227502, A227848.

Sequence in context: A025633 A249697 A038287 * A343186 A041140 A195940

Adjacent sequences: A229092 A229093 A229094 * A229096 A229097 A229098

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