A376212 a(n) is the least k such that A001615(k) = 2*n, or -1 if there is no such k, where A001615 is the Dedekind psi function.

-1, 3, 4, 7, -1, 6, 13, -1, 10, 19, -1, 12, -1, -1, 25, 21, -1, 18, 37, -1, 26, 43, -1, 24, -1, -1, 34, 39, -1, 38, 61, -1, -1, 67, -1, 30, 73, -1, -1, 57, -1, 52, -1, -1, 50, -1, -1, 42, 97, -1, 101, 103, -1, 54, 109, 91, 74, -1, -1, 75, -1, -1, 82, 93, -1, 86, -1, -1, 137, 139, -1, 60, -1, -1

Offset: 1

Author

Robert Israel, Sep 15 2024

Keywords

• sign
• look

Comments

Since A001615(k) > k for k > 1, a(n) < 2*n.

Examples

			a(3) = 4 because A001615(4) = 6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001615, A203444, A291487.

Programs

Maple

psi:= proc(n) local p;
   n * mul(1+1/p, p = numtheory:-factorset(n))
end proc:
N:= 100: # for a(1) to a(N)
V:= Vector(N,-1):
for k from 3 to 2*N-1 do
 v:= psi(k)/2;
   if v <= N and V[v] = -1 then V[v]:= k fi
od:
convert(V,list);