

A340482


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.


3



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

1,1


COMMENTS

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.
p^2 is a term iff p is in A048161, and this subsequence of p^2 is A263951.  Bernard Schott, Jan 10 2021


LINKS

Table of n, a(n) for n=1..53.


EXAMPLE

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 ).


MATHEMATICA

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]


PROG

(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


CROSSREFS

Union of A128283 and A263951.
Subsequence of A046315 (all odd semiprimes).
Cf. A048161, A070552, A128281, A237591, A237593, A249223, A262045, A340482.
Sequence in context: A272600 A327862 A108181 * A324722 A295230 A273202
Adjacent sequences: A340479 A340480 A340481 * A340483 A340484 A340485


KEYWORD

nonn


AUTHOR

Hartmut F. W. Hoft, Jan 09 2021


STATUS

approved



