A322840 Positive integers n with fewer prime factors (counted with multiplicity) than n + 1.

1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 26, 29, 31, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 59, 61, 62, 63, 65, 67, 69, 71, 73, 74, 77, 79, 83, 87, 89, 91, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 119, 123, 125, 127, 129, 131, 134, 137, 139, 143, 146, 149

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

49 = 7*7 has two prime factors, while 50 = 2*5*5 has three, so 49 belongs to the sequence.

Mathematica

Select[Range[100], PrimeOmega[#]<PrimeOmega[#+1]&]
Position[Partition[PrimeOmega[Range[150]], 2, 1], _?(#[[1]]< #[[2]]&), 1, Heads->False]//Flatten (* Harvey P. Dale, Sep 23 2021 *)

Prog

(PARI) isok(n) = bigomega(n) < bigomega(n+1); \\ Michel Marcus, Dec 29 2018

Crossrefs

Cf. A001222, A006049, A045920, A294277, A294278, A302242, A322837, A322838, A322839.

Sequence in context: A325570 A210719 A353685 * A336374 A346669 A187929

Adjacent sequences: A322837 A322838 A322839 * A322841 A322842 A322843

Keyword

nonn

Author

Gus Wiseman, Dec 28 2018

Status

approved