A328926 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

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.

PROG

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

CROSSREFS

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

Sequence in context: A264964 A374918 A195064 * A055743 A354424 A189680

Adjacent sequences: A328923 A328924 A328925 * A328927 A328928 A328929

KEYWORD

nonn

AUTHOR

Jianing Song, Oct 31 2019

STATUS

approved