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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A216679 A216680 A162283 * A211144 A213386 A041404

Adjacent sequences:  A180325 A180326 A180327 * A180329 A180330 A180331

KEYWORD

nonn

AUTHOR

T. D. Noe, Sep 07 2010

STATUS

approved

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Last modified November 22 09:35 EST 2017. Contains 295076 sequences.