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A037143
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Numbers with at most 2 prime factors (counted with multiplicity).
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68
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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
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OFFSET
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1,2
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COMMENTS
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Also, numbers with permutations of all divisors only with coprime adjacent elements: A109810(a(n)) > 0. - Reinhard Zumkeller, May 24 2010
1 together with numbers k such that sigma(k) + phi(k) - d(k) = 2k - 2. - Wesley Ivan Hurt, May 03 2015
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LINKS
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MAPLE
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MATHEMATICA
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Select[Range[120], PrimeOmega[#] <= 2 &] (* Ivan Neretin, Aug 16 2015 *)
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PROG
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(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
(Python)
from math import isqrt
from sympy import primepi, primerange
def f(x): return int(n-2+x-primepi(x)-sum(primepi(x//k)-a for a, k in enumerate(primerange(isqrt(x)+1))))
kmin, kmax = 1, 2
while f(kmax) >= kmax:
kmax <<= 1
while True:
kmid = kmax+kmin>>1
if f(kmid) < kmid:
kmax = kmid
else:
kmin = kmid
if kmax-kmin <= 1:
break
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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