OFFSET
1,1
COMMENTS
Complement to A055932.
From Michael De Vlieger, Feb 06 2024: (Start)
Odd prime power p^m, m >= 1 is in the sequence since its squarefree kernel p is odd and not a primorial. Therefore 3^3, 5^2, etc. are in the sequence.
Odd squarefree composite k is in the sequence since its squarefree kernel is odd and thus not a primorial. Therefore 15 and 33 are in the sequence.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
From Michael De Vlieger, Jan 23 2024: (Start)
1 is not in the sequence because its squarefree kernel is 1, the product of the 0 primes that divide 1 (the "empty product") and therefore the same as A002110(0), the 0th primorial.
2 is not in the sequence since its squarefree kernel is 2, the smallest prime, hence the same as A002110(1) = 2.
4 is not in the sequence since its squarefree kernel is 2 = A002110(1).
(End)
MATHEMATICA
Select[Range[120], Nor[IntegerQ@ Log2[#], And[EvenQ[#], Union@ Differences@ PrimePi[FactorInteger[#][[All, 1]]] == {1}]] &] (* Michael De Vlieger, Jan 23 2024 *)
PROG
(PARI) is(n) = {my(f=factor(n)[, 1]); n>1&&primepi(f[#f])>#f} \\ David A. Corneth, May 22 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 19 2003
EXTENSIONS
Edited by Michael De Vlieger, Jan 23 2024
STATUS
approved