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A073493
Numbers having exactly one prime gap in their factorization.
21
10, 14, 20, 21, 22, 26, 28, 33, 34, 38, 39, 40, 42, 44, 46, 50, 51, 52, 55, 56, 57, 58, 62, 63, 65, 66, 68, 69, 70, 74, 76, 78, 80, 82, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 98, 99, 100, 102, 104, 106, 111, 112, 114, 115, 116, 117, 118, 119, 122, 123, 124, 126, 129
OFFSET
1,1
LINKS
FORMULA
A073490(a(n)) = 1.
EXAMPLE
200 is a term, as 200 = 2*2*2*5*5 with one gap between 2 and 5.
MATHEMATICA
pa[n_, k_] := If[k == NextPrime[n], 0, 1]; Select[Range[130], Total[pa @@@ Partition[First /@ FactorInteger[#], 2, 1]] == 1 &] (* Jayanta Basu, Jul 01 2013 *)
PROG
(Haskell)
a073493 n = a073493_list !! (n-1)
a073493_list = filter ((== 1) . a073490) [1..]
-- Reinhard Zumkeller, Dec 20 2013
(Python)
from sympy import primefactors, nextprime
def ok(n):
pf = primefactors(n)
return sum(p2 != nextprime(p1) for p1, p2 in zip(pf[:-1], pf[1:])) == 1
print(list(filter(ok, range(1, 130)))) # Michael S. Branicky, Oct 14 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 03 2002
STATUS
approved