A227429 Numbers k such that Sum_{j=1..k} j^phi(j) == 0 (mod k).

1, 3, 4, 12, 21, 39, 91, 156, 381, 1668, 3292, 4541, 6515, 12927, 49492, 72412, 100595, 158708

Offset: 1

Author

Paolo P. Lava, Jul 11 2013

Keywords

• nonn
• more

Comments

a(17) > 10^5. - Giovanni Resta, Jul 11 2013

a(19) > 2473000. - Kevin P. Thompson, Nov 28 2021

Examples

			4 is a member of the sequence since Sum_{j=1..4} j^phi(j) = 1^phi(1) + 2^phi(2) + 3^phi(3) + 4^phi(4) = 1^1 + 2^1 + 3^2 + 4^2 = 28 which is divisible by 4.
		

Crossrefs

Cf. A000010, A227427.

Programs

Maple

with(numtheory); ListA227429:=proc(q) local i,n;
for n from 1 to q do if add(i^phi(i),i=1..n) mod n=0 then print(n);
fi; od; end: ListA227429(10^6);

Extensions

a(10)-a(16) from Giovanni Resta, Jul 11 2013

a(17)-a(18) from Kevin P. Thompson, Nov 28 2021