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A340482
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Numbers that are the product of two not necessarily distinct odd primes p*q with the property that (p*q+1)/2 and (p+q)/2 are primes.
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3
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9, 21, 25, 33, 57, 85, 93, 121, 133, 145, 177, 205, 213, 217, 253, 361, 393, 445, 553, 565, 633, 697, 793, 817, 841, 865, 913, 933, 973, 1137, 1285, 1345, 1417, 1437, 1465, 1477, 1513, 1537, 1717, 1765, 1837, 1857, 1893, 2101, 2173, 2245, 2305, 2517, 2577, 2581, 2605, 2641, 2653
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OFFSET
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1,1
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COMMENTS
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For the squares p^2 in this sequence the area of the central region of the three regions in the symmetric representation of sigma(p^2) is equal to p.
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LINKS
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EXAMPLE
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a(1) = 9 = 3*3 is the first number for which SRS(a(1)) consists of three regions ( 5, 3, 5 ).
a(6) = 85 = 5*17, both (1+85)/2 = 43 and (5+17)/2 = 11 are primes, and SRS(a(6)) consists of the 4 regions ( 43, 11, 11, 43 ).
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MATHEMATICA
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dQ[s_] := Module[{d=Divisors[s]}, AllTrue[Map[(d[[#]]+d[[-#]])/2&, Range[Length[d]/2]], PrimeQ]]
a340482[n_] := Select[Range[n], PrimeOmega[#]==2&&dQ[#]&]
a340482[2700]
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PROG
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(PARI) isok(m) = if ((m % 2) && (bigomega(m)==2), if (issquare(m), isprime((m+1)/2), my(p=factor(m)[1, 1], q=factor(m)[2, 1]); isprime((p*q+1)/2) && isprime((p+q)/2))); \\ Michel Marcus, Jan 10 2021
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CROSSREFS
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Subsequence of A046315 (all odd semiprimes).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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