A355714 Numbers k > 0 such that A090252(A355176(k)) does not equal prime(k)^2.

1, 2, 16, 26, 32, 35, 40, 59, 60, 69, 92, 105, 110, 112, 113, 137, 167, 169, 178, 185, 186, 188, 207, 210, 260, 261, 274, 287, 289, 342, 344, 346, 356, 357, 359, 361, 362, 363, 391, 412, 417, 434, 457, 477, 478, 479, 480, 481, 492, 547, 563, 598, 663, 666, 671

Offset: 1

Author

Thomas Scheuerle, Jul 15 2022

Keywords

• nonn

Comments

In contrast to A354169 (a set theoretic analog of A090252) where we observe many as yet unproved regularities, in A090252 the situation appears to be more complicated. This sequence is intended to help spot these irregularities and perhaps lead to further rules, which probably have no analogy in A354169.

In most cases A090252(A355176(n)) equals prime(a(n))*p where p is prime. Surprisingly p is in many cases greater than prime(a(n)).

Is this sequence infinite?

Crossrefs

Cf. A000040, A001248, A090252, A354169, A355176.

Formula

A090252(A355176(a(n))) <> A000040(a(n))^2.

A000040(a(n)) divides A090252(A355176(a(n))).

A000040(a(n)) divides A090252(2*A355176(a(n))+1).

Extensions

More terms from Jinyuan Wang, Jul 15 2022