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A073493 Numbers having exactly one prime gap in their factorization. 8
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 (list; graph; refs; listen; history; text; internal format)
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 A251727

Adjacent sequences:  A073490 A073491 A073492 * A073494 A073495 A073496

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 03 2002

STATUS

approved

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Last modified May 18 22:37 EDT 2022. Contains 353826 sequences. (Running on oeis4.)