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A220218 Numbers where all exponents in its prime factorization are one less than a prime. 3
1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sequence has positive density, between 0.83 and 0.89; probably about 0.87951.

LINKS

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

P. Erdős and L. Mirsky, The distribution of values of the divisor function d(n), Proc. London Math. Soc. 2 (1952), pp. 257-271.

MATHEMATICA

Select[Range[100], AllTrue[Transpose[FactorInteger[#]][[2]]+1, PrimeQ]&] (* Harvey P. Dale, Sep 29 2014 *)

PROG

(PARI) is(n)=vecmin(apply(n->isprime(n+1), factor(max(n, 2))[, 2])) \\ Charles R Greathouse IV, Dec 07 2012

(Haskell)

a220218 n = a220218_list !! (n-1)

a220218_list = 1 : filter

               (all (== 1) . map (a010051' . (+ 1)) . a124010_row) [1..]

-- Reinhard Zumkeller, Nov 30 2015

CROSSREFS

Apart from the first term, a subsequence of A096432.

Cf. A010051, A124010.

Sequence in context: A219227 A007412 A270420 * A096432 A138302 A270428

Adjacent sequences:  A220215 A220216 A220217 * A220219 A220220 A220221

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Dec 07 2012

STATUS

approved

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Last modified October 17 05:23 EDT 2018. Contains 316275 sequences. (Running on oeis4.)