A180328 Semiprimes pq such that there is another semiprime rs with (p+1)(q+1)=(r+1)(s+1) and p, q, r, and s distinct primes.

14, 15, 33, 35, 46, 51, 55, 62, 69, 77, 87, 94, 95, 115, 118, 119, 123, 141, 142, 143, 145, 155, 158, 159, 161, 166, 177, 187, 203, 205, 209, 213, 214, 221, 235, 249, 253, 254, 265, 267, 278, 287, 295, 299, 302, 303, 319, 321, 323, 329, 334, 335, 339, 341, 355

Offset

1,1

Comments

Note that for a semiprime p*q, the expression (p+1)*(q+1) is the sum of the divisors (A000203) of p*q. - Michel Marcus, Jan 29 2015

Subsequence of A162283. - Gionata Neri, Nov 20 2015

Links

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

Example

For pq = 14 = 2*7, the corresponding rs is 15 because (2+1)(7+1) = 24 = (3+1)(5+1).

Mathematica

nn=1000; sp=Select[Range[2, 3*nn/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. A000203, A180329 (odd semiprimes with this property).

Sequence in context: A216680 A332736 A162283 * A211144 A213386 A370403

Adjacent sequences: A180325 A180326 A180327 * A180329 A180330 A180331

Keyword

nonn

Author

T. D. Noe, Sep 07 2010

Status

approved