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A376352
Squarefree semiprimes k such that k+1 is the product of three distinct primes and k+2 is the product of four distinct primes.
1
2413, 6193, 6697, 9469, 11065, 11233, 11893, 12153, 13333, 13393, 14005, 14089, 14233, 15293, 17113, 17533, 17833, 17869, 18613, 18653, 19693, 20053, 20557, 20613, 20733, 20893, 20993, 21145, 22033, 22285, 22405, 22693, 22753, 22969, 23329, 23413, 24033, 24493, 26101, 26453, 27113, 27553, 28117, 28453, 28741, 29053, 29353, 29713
OFFSET
1,1
LINKS
FORMULA
a(n) == 1 (mod 4).
EXAMPLE
2413 is a term because 2413 = 19*127 is the product of two distinct primes, 2414 = 2*17*71 is the product of three distinct primes and 2415 = 3*5*7*23 is the product of four distinct primes.
6193 is a term because 6193 = 11*563 is the product of two distinct primes, 6194 = 2*19*163 is the product of three distinct primes and 6195 = 3*5*7*59 is the product of four distinct primes.
MAPLE
q:= n-> andmap(j-> map(i-> i[2], ifactors(n+j-2)[2])=[1$j], [$2..4]):
select(q, [$1..30000])[]; # Alois P. Heinz, Sep 21 2024
MATHEMATICA
Position[Partition[FactorInteger[#][[;; , 2]] & /@ Range[30000], 3, 1], {{1, 1}, {1, 1, 1}, {1, 1, 1, 1}}] // Flatten (* Amiram Eldar, Sep 21 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Massimo Kofler, Sep 21 2024
STATUS
approved