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.

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

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 * A367782 A356765 A020260

Adjacent sequences: A180326 A180327 A180328 * A180330 A180331 A180332

Keyword

nonn

Author

T. D. Noe, Sep 07 2010

Status

approved