A162643 - OEIS (original) (raw)

4, 9, 12, 16, 18, 20, 25, 28, 32, 36, 44, 45, 48, 49, 50, 52, 60, 63, 64, 68, 72, 75, 76, 80, 81, 84, 90, 92, 96, 98, 99, 100, 108, 112, 116, 117, 121, 124, 126, 132, 140, 144, 147, 148, 150, 153, 156, 160, 162, 164, 169, 171, 172, 175, 176, 180, 188, 192, 196, 198

COMMENTS

A number m is a term if and only if it has at least one non-infinitary divisor, or A000005(m) > A037445(m). - Vladimir Shevelev, Feb 23 2017

The asymptotic density of this sequence is 1 - A327839 = 0.3121728605... - Amiram Eldar, Jul 28 2020

MATHEMATICA

Select[Range@ 192, ! IntegerQ@ Log2@ DivisorSigma[0, #] &] (* Michael De Vlieger, Feb 24 2017 *)

PROG

(Haskell)

a162643 n = a162643_list !! (n-1)

a162643_list = filter ((== 0) . a209229 . a000005) [1..]

(Python)

from itertools import count, islice

from sympy import factorint

def A162643_gen(startvalue=1): # generator of terms >= startvalue

return filter(lambda n:any(map(lambda m:((k:=m+1)&-k)^k, factorint(n).values())), count(max(startvalue, 1)))