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Lesser of twin primes p such that d(p+1) > d(q+1) for all lessers of twin primes q < p, where d(n) is the number of divisors of n (A000005).
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%I #5 Oct 12 2019 19:08:44

%S 3,5,11,29,59,179,239,419,1319,2339,3119,3359,6299,7559,21599,21839,

%T 33599,35279,42839,55439,100799,110879,287279,415799,957599,1621619,

%U 1713599,1867319,1940399,2489759,3991679,6652799,11531519,18258239,22822799,26732159,28828799

%N Lesser of twin primes p such that d(p+1) > d(q+1) for all lessers of twin primes q < p, where d(n) is the number of divisors of n (A000005).

%C The corresponding values of d(p+1) are 3, 4, 6, 8, 12, 18, 20, 24, 32, 36, 40, 48, 54, 64, 72, 80, 84, 90, 96, 120, 126, 144, 160, 192, 216, 240, 252, 256, 270, 288, 320, 384, 432, 448, 480, 512, 576, ...

%t dm = DivisorSigma[0, 4]; s = {3}; Do[If[!PrimeQ[6n - 1] || !PrimeQ[6n + 1], Continue[]]; d = DivisorSigma[0, 6n]; If[d > dm, dm = d; AppendTo[s, 6n - 1]], {n, 1, 10^5}]; s

%Y Cf. A000005, A001359, A068507, A321995, A326392.

%K nonn

%O 1,1

%A _Amiram Eldar_, Oct 12 2019