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A046388 Odd numbers of the form p*q where p and q are distinct primes. 76
15, 21, 33, 35, 39, 51, 55, 57, 65, 69, 77, 85, 87, 91, 93, 95, 111, 115, 119, 123, 129, 133, 141, 143, 145, 155, 159, 161, 177, 183, 185, 187, 201, 203, 205, 209, 213, 215, 217, 219, 221, 235, 237, 247, 249, 253, 259, 265, 267, 287, 291, 295, 299, 301, 303 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These are the odd squarefree semiprimes.

These numbers n have the property that n is a Fermat pseudoprime for at least two bases 1 < b < n - 1. That is, b^(n - 1) == 1 (mod n). See sequence A175101 for a count of the number of bases. - Karsten Meyer, Dec 02 2010

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

FORMULA

Sum_{n>=1} 1/a(n)^s = (1/2)*(P(s)^2 - P(2*s)) + 1/4^s - P(s)/2^s, for s>1, where P is the prime zeta function. - Amiram Eldar, Nov 21 2020

MATHEMATICA

max = 300; A046388 = Sort@Flatten@Table[Prime[m] Prime[n], {n, 3, Ceiling[PrimePi[max/3]]}, {m, 2, n - 1}]; Select[A046388, # < max &] (* Alonso del Arte based on Robert G. Wilson v's program for A006881, Oct 24 2011 *)

PROG

(Haskell)

a046388 n = a046388_list !! (n-1)

a046388_list = filter ((== 2) . a001221) a056911_list

-- Reinhard Zumkeller, Jan 02 2014

(PARI) isok(n) = (n % 2) && (bigomega(n) == 2) && (omega(n)==2); \\ Michel Marcus, Feb 05 2015

CROSSREFS

Intersection of A005117 and A046315.

Subsequence of A024556. - Zak Seidov, May 28 2020

Cf. A001358, A046404.

Different from A056913, A098905, A225375.

Cf. A001221, A056911.

Sequence in context: A329229 A146166 A024556 * A056913 A002557 A128907

Adjacent sequences:  A046385 A046386 A046387 * A046389 A046390 A046391

KEYWORD

nonn

AUTHOR

Patrick De Geest, Jun 15 1998

EXTENSIONS

I removed some ambiguity in the definition and edited the entry, merging in some material from A146166. - N. J. A. Sloane, May 09 2013

STATUS

approved

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Last modified June 14 07:10 EDT 2021. Contains 345018 sequences. (Running on oeis4.)