A280383 Numbers n such that n-1 has the same count of prime factors as n+1 when including multiplicity and also when not.

4, 6, 12, 18, 19, 30, 34, 42, 51, 55, 56, 60, 72, 86, 92, 94, 102, 108, 138, 142, 144, 150, 160, 180, 184, 186, 192, 198, 202, 204, 214, 216, 218, 220, 228, 236, 240, 243, 248, 249, 266, 270, 282, 300, 302, 304, 307, 312, 320, 322, 328, 340, 341, 348, 349, 392, 394, 412, 414, 416, 420, 424, 432, 446, 452, 462, 470, 472, 476, 491, 516, 518, 522, 534, 536, 544, 552, 570, 580, 582, 590, 600, 604, 618, 634, 638, 642, 660, 664, 668, 670, 680, 686, 688, 696, 698, 701, 722

Offset: 1

Author

Rick L. Shepherd, Jan 02 2017

Keywords

• nonn

Comments

First differs from its subsequence A074997 at a(97) = 701 because A074997(97) = 722.

Examples

			The number 19 is a term because 18 = 2*3^2 and 20 = 2^2*5 each have two distinct prime factors and each have three prime factors when counted with multiplicity.
		

Links

• Rick L. Shepherd, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A001222, A074997, A088070, A280382.

Programs

Mathematica

Select[Range[800],PrimeNu[#]==PrimeNu[#+2]&&PrimeOmega[#]==PrimeOmega[#+2]&]+1 (* Harvey P. Dale, Jul 12 2023 *)

PARI

IsInA280383(n) = n > 1 && bigomega(n-1) == bigomega(n+1) && omega(n-1) == omega(n+1)

Formula

Sequence is A088070 INTERSECT A280382.