A073493 Numbers having exactly one prime gap in their factorization.

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

Cf. A005117, A073490, A073492, A073494, A073495, A073487.

Sequence in context: A307516 A069900 A073492 * A162685 A272374 A362982

Adjacent sequences: A073490 A073491 A073492 * A073494 A073495 A073496

Keyword

nonn

Author

Reinhard Zumkeller, Aug 03 2002

Status

approved