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

1,1

Comments

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

Links

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

Formula

Sequence is A088070 INTERSECT A280382.

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A301166 A310599 A074997 * A045959 A310600 A296507

Adjacent sequences: A280380 A280381 A280382 * A280384 A280385 A280386

Keyword

nonn

Author

Rick L. Shepherd, Jan 02 2017

Status

approved