OFFSET
1,1
COMMENTS
Numbers with one or more 1's, exactly one 2 and no 3's or higher in their prime exponents. - Antti Karttunen, Sep 19 2019
From Salvador Cerdá, Mar 08 2016: (Start)
12!+1 = 13^2 * 2834329 is in this sequence.
23!+1 = 47^2 * 79 * 148139754736864591 is also in this sequence. (End)
The asymptotic density of this sequence is (6/Pi^2) * Sum_{p prime} 1/(p*(p+1)) (A271971). - Amiram Eldar, Nov 09 2020
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000 ( 1..100 from Paolo P. Lava)
EXAMPLE
a(14) = 84 = 7*3*2^2; the following numbers are not terms: 36=6^2, as it is a square; 54=2*3^3, as it is not cubefree; 42=2*3*7, as there is no squared prime; 72=2*6^2, as 72 has two squared prime divisors: 2^2 and 3^2.
MAPLE
N:= 1000: # to get all terms <= N
Primes:= select(isprime, [$2..floor(N^(1/2))]):
SF:= select(numtheory:-issqrfree, [$2..N/4]):
S:= {seq(op(map(p -> p^2*t, select(s -> igcd(s, t)=1 and s^2*t <= N, Primes))), t = SF)}:
sort(convert(S, list)); # Robert Israel, Mar 08 2016
MATHEMATICA
Select[Range@ 308, And[PrimeNu@ # > 1, PrimeOmega@ # - PrimeNu@ # == 1] &] (* Michael De Vlieger, Mar 09 2016 *)
PROG
(PARI) isok(n) = (omega(n) > 1) && (bigomega(n) - omega(n) == 1); \\ Michel Marcus, Jul 16 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 18 2002
STATUS
approved