A344655 Numbers k such that A032741(k-1)+A065608(k+1) is divisible by k.

1, 2, 5, 7, 32767

Offset: 1

Author

J. M. Bergot and Robert Israel, May 25 2021

Keywords

• nonn
• more

Comments

Numbers k such that Sum_{j|k-1} (k mod j) + Sum_{j|k+1} (k mod j) is divisible by k.

a(6) > 10^8 if it exists.

Examples

			a(5) = 32767 is a term because A032741(32767-1)+A065608(32768+1) = 15+65519 = 65534 = 2*32767.
		

Crossrefs

Cf. A032741, A065608.

Programs

Maple

filter:= proc(p) local d;
(numtheory:-tau(p-1) + numtheory:-sigma(p+1) - numtheory:-tau(p+1)-1) mod p = 0
end proc:
select(filter, [$1..10^5]);