A369139 Numbers k such that Omega(k) = 1 + Omega(k + 1).

4, 6, 8, 10, 20, 22, 45, 46, 50, 58, 68, 76, 80, 82, 92, 104, 105, 106, 110, 114, 117, 152, 154, 165, 166, 178, 182, 186, 189, 212, 226, 236, 246, 258, 260, 261, 262, 266, 273, 286, 290, 315, 318, 322, 325, 333, 338, 342, 344, 345, 346, 354, 357, 358, 370, 382, 385, 402, 406, 410, 412, 424, 426

Offset: 1

Author

Zak Seidov and Robert Israel, Jan 14 2024

Keywords

• nonn

Comments

Numbers k that have one more prime divisor (counted by multiplicity) than k + 1.

Examples

			a(3) = 8 is a term because 8 = 2^3 has 3 prime divisors (counted by multiplicity) and 8 + 1 = 9 = 3^2 has 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A045920, A076156. Contains A077065.

Programs

Maple

N:= 1000: # for terms <= N
V:= map(numtheory:-bigomega, [$1..N+1]):
select(t -> V[t] = 1 + V[t+1], [$1..N]);

Mathematica

s = {}; Do[If[PrimeOmega[k] == 1 + PrimeOmega[k + 1], AppendTo[s, k]], {k, 500}]; s