A037143 Numbers with at most 2 prime factors (counted with multiplicity).

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118

Offset

1,2

Comments

A001222(a(n)) <= 2; A054576(a(n)) = 1. - Reinhard Zumkeller, Mar 10 2006

Products of two noncomposite numbers. - Juri-Stepan Gerasimov, Apr 15 2010

Also, numbers with permutations of all divisors only with coprime adjacent elements: A109810(a(n)) > 0. - Reinhard Zumkeller, May 24 2010

A060278(a(n)) = 0. - Reinhard Zumkeller, Apr 05 2013

1 together with numbers k such that sigma(k) + phi(k) - d(k) = 2k - 2. - Wesley Ivan Hurt, May 03 2015

Products of two not necessarily distinct terms of A008578 (the same relation between A000040 and A001358). - Flávio V. Fernandes, May 28 2021

Links

Felix Fröhlich, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)

Andreas Weingartner, Uniform distribution of alpha*n modulo one for a family of integer sequences, arXiv:2303.16819 [math.NT], 2023.

Maple

with(numtheory): A037143:=n->`if`(bigomega(n)<3, n, NULL): seq(A037143(n), n=1..200); # Wesley Ivan Hurt, May 03 2015

Mathematica

Select[Range[120], PrimeOmega[#] <= 2 &] (* Ivan Neretin, Aug 16 2015 *)

Prog

(Haskell)
a037143 n = a037143_list !! (n-1)
a037143_list = 1 : merge a000040_list a001358_list where
   merge xs'@(x:xs) ys'@(y:ys) =
         if x < y then x : merge xs ys' else y : merge xs' ys
-- Reinhard Zumkeller, Dec 18 2012
(PARI) is(n)=bigomega(n)<3 \\ Charles R Greathouse IV, Apr 29 2015

Crossrefs

Union of A008578 and A001358. Complement of A033942.

Cf. A063928, A001222, A054576, A109810, A060278.

A101040(a(n))=1 for n>1.

Subsequence of A037144. - Reinhard Zumkeller, May 24 2010

A098962 and A139690 are subsequences.

Sequence in context: A325457 A063538 A167207 * A236105 A292050 A048627

Adjacent sequences: A037140 A037141 A037142 * A037144 A037145 A037146

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Henry Bottomley, Aug 15 2001

Status

approved