|
%I #27 Jan 10 2021 22:12:12
%S 9,21,25,33,57,85,93,121,133,145,177,205,213,217,253,361,393,445,553,
%T 565,633,697,793,817,841,865,913,933,973,1137,1285,1345,1417,1437,
%U 1465,1477,1513,1537,1717,1765,1837,1857,1893,2101,2173,2245,2305,2517,2577,2581,2605,2641,2653
%N 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.
%C 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.
%C p^2 is a term iff p is in A048161, and this subsequence of p^2 is A263951. - _Bernard Schott_, Jan 10 2021
%e a(1) = 9 = 3*3 is the first number for which SRS(a(1)) consists of three regions ( 5, 3, 5 ).
%e 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 ).
%t dQ[s_] := Module[{d=Divisors[s]}, AllTrue[Map[(d[[#]]+d[[-#]])/2&, Range[Length[d]/2]], PrimeQ]]
%t a340482[n_] := Select[Range[n], PrimeOmega[#]==2&&dQ[#]&]
%t a340482[2700]
%o (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
%Y Union of A128283 and A263951.
%Y Subsequence of A046315 (all odd semiprimes).
%Y Cf. A048161, A070552, A128281, A237591, A237593, A249223, A262045, A340482.
%K nonn
%O 1,1
%A _Hartmut F. W. Hoft_, Jan 09 2021
|
