A229095 - OEIS

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

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OFFSET

1,2

LINKS

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);

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

a(16)-a(18) from Jinyuan Wang, Feb 18 2021

STATUS

approved