

A180329


Odd semiprimes pq such that there is another odd semiprime rs with (p+1)(q+1)=(r+1)(s+1) and p, q, r, and s distinct primes.


2



33, 35, 51, 55, 69, 77, 87, 95, 115, 119, 123, 141, 143, 155, 159, 161, 177, 187, 203, 205, 209, 213, 221, 235, 249, 253, 267, 287, 295, 299, 303, 319, 321, 323, 329, 335, 339, 341, 355, 371, 391, 393, 395, 407, 413, 415, 437, 445, 447, 451, 473, 485, 493
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OFFSET

1,1


COMMENTS

These numbers are related to amicable pairs of the form (G * pq, G * rs), where G is coprime to pq and rs. The interesting case of G=2^n is shown in A180330.


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000


EXAMPLE

For pq = 33 = 3*11, the corresponding rs is 35 because (3+1)(11+1) = 48 = (5+1)(7+1).


MATHEMATICA

nn=1000; sp=Select[Range[3, 4*nn/3, 2], Last/@FactorInteger[ # ]=={1, 1}&]; prods=Table[Times@@(1+First/@FactorInteger[n]), {n, sp}]; dups=Select[Tally[prods], #[[2]]>1&]; goodProds=Sort[Transpose[dups][[1]]]; pos=Select[Range[Length[sp]], sp[[ # ]]<=nn && MemberQ[goodProds, prods[[ # ]]]&]; sp[[pos]]


CROSSREFS

Cf. A180328 (all semiprimes with this property)
Sequence in context: A140143 A041543 A144425 * A020260 A140147 A223733
Adjacent sequences: A180326 A180327 A180328 * A180330 A180331 A180332


KEYWORD

nonn


AUTHOR

T. D. Noe, Sep 07 2010


STATUS

approved



