

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
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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 !! (n1)
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



