A341015 Numbers k such that A124446(k) = 1.

1, 2, 3, 4, 5, 6, 9, 18, 25, 27, 54, 81, 125, 162, 243, 486, 625, 729, 1458, 2187, 3125, 4374, 6561, 13122, 15625, 19683, 39366, 59049, 78125, 118098, 177147, 354294, 390625, 531441, 1062882, 1594323, 1953125, 3188646, 4782969, 9565938, 9765625, 14348907, 28697814

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 02 2021

Keywords

• nonn

Comments

Numbers k such that A066840(k) and A124440(k) are coprime.

Contains all numbers of the forms 3^j, 2*3^j and 5^j.

Conjecture: the only term not of one of those forms is 4.

Examples

			18 is a term because A066840(18) = 13 and A124440(18) = 41 are coprime.
		

Crossrefs

Cf. A066840, A124440, A124446.

Programs

Maple

N:= 2*10^4: # for terms <= N
G:= add(numtheory:-mobius(n)*n*x^(2*n)/((1-x^n)*(1-x^(2*n))^2),n=1..N/2):
S:= series(G,x,N+1):
A66840:= [seq(coeff(S,x,j),j=1..N)]:
filter:= n -> igcd(A66840[n], n*numtheory:-phi(n)/2)=1:
filter(1):= true:
select(filter, [$1..N]);

Formula

A124446(a(n)) = 1.

Extensions

More terms from Jinyuan Wang, Feb 07 2021