A328926 Numbers k such that A328925(k) = 1; numbers k such that if we write k = Product_{i=1..t} p_i^e_i, then lcm_{1<=i,j<=t,i!=j} ord(p_i,p_j^e_j) = A002322(k), where ord(a,r) is the multiplicative order of a modulo r, and A002322 is the Carmichael lambda (usually written as psi).

1, 2, 6, 10, 12, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 35, 36, 38, 40, 42, 44, 45, 48, 50, 51, 52, 54, 56, 57, 58, 60, 63, 66, 69, 70, 72, 74, 75, 76, 77, 78, 80, 84, 85, 87, 88, 90, 91, 92, 93, 96, 99, 100, 102, 104, 105, 106, 108, 110, 114, 115, 116, 118, 119, 120, 122

Offset: 1

Author

Jianing Song, Oct 31 2019

Keywords

• nonn

Comments

Numbers such that A118106(k) = A002322(k).

{a(n)} intersect A000961 = {1, 2}.

{a(n)} union A329062 = N* \ A000961 U {1, 2}.

If k = Product_{i=1..t} p_i^e_i (t > 1), where {p_i} are primes such that p_i is a lambda primitive root modulo p_j^e_j for all i != j (that is to say, ord(p_i,p_j^e_j) = A002322(p_j^e_j), where ord(a,r) is the multiplicative order of a modulo r), then k is here, as A118106(k) = A002322(k). For example, k = 2^5 * 5 * 13.

Examples

			For k = 115 = 5 * 23, A118106(115) = lcm(ord(23,5),ord(5,23)) = lcm(4,22) = 44 = A002322(115), so 115 is a term.
For k = 973 = 7 * 139, A118106(973) = lcm(ord(139,7),ord(7,139)) = lcm(6,69) = 138 = A002322(973), so 973 is a term.
		

Crossrefs

Cf. A118106, A002322, A326925, A329062, A000961.

Programs

PARI

isA328926(n) = (A002322(n) == A118106(n)) \\ See A002322 and A118106 for their programs