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n such that A193453(n) is different of A193169(n).

Numbers n such that A000265(lambda(n)) < A000265(phi(n)), where A000265(m) is the odd part (largest odd divisor) of m. - Amiram Eldar and Thomas Ordowski, Feb 04 2019

From Jianing Song, Oct 19 2021: (Start)

Let G = (Z/kZ)* be the multiplicative group of integers modulo k and G_2 be the Sylow 2-subgroup of G. Sequence lists k such that G/G_2 is not cyclic; equivalently, decompose G as a product of cyclic groups C_{k_1} x C_{k_2} x ... x C_{k_m}, where k_i divides k_j for i < j, then k is a term if and only if m > 1 and k_{m-1} is not a power of 2.

Numbers k such that there exists an odd prime p such that the p-rank of G is greater than 1. (The rank of a finitely generated group rank(G) is defined to be the size of the minimal generating sets of G, and the p-rank of G is the rank of the Sylow p-subgroup of G.)

k is a term if and only if k satisfies at least one of the two conditions: (a) there exists an odd prime p such that k has two distinct prime factors congruent to 1 modulo p (for example 91 = 7 * 13, 7 == 13 == 1 (mod 3)); (b) there exists an odd prime p such that k has a prime factor congruent to 1 modulo p and that k is divisible by p^2 (for example 275 = 11 * 5^2, 11 == 1 (mod 5)). (End)