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Number of brilliant numbers < 10^n.
2

%I #14 Apr 09 2022 13:22:38

%S 3,10,73,241,2504,10537,124363,573928,7407840,35547994,491316166,

%T 2409600865,34896253009,174155363186,2601913448896,13163230391312,

%U 201431415980418,1029540512731472

%N Number of brilliant numbers < 10^n.

%o (PARI) a(n) = my(N=10^n-1, count=0, L=#digits(sqrtint(N))); for(k=1, L-1, count += binomial(primepi(10^k) - primepi(10^(k-1)) + 1, 2)); my(min = 10^(L-1), max = 10^L-1, pi_min = primepi(min), pi_max = primepi(max), j = 0); forprime(p = min, max, if(p*p <= N, count += if(N >= p*max, pi_max, primepi(N\p)) - pi_min - j; j+=1, break)); count; \\ _Daniel Suteu_, Apr 09 2022

%Y Cf. A078972, A087434, A087435.

%K nonn,more

%O 1,1

%A _Jason Earls_, Aug 09 2003

%E More terms from _Ray Chandler_, Aug 31 2003

%E a(11)-a(14) from _Ray Chandler_, Jul 21 2005

%E a(15)-a(16) from _Donovan Johnson_, May 30 2010

%E a(17)-a(18) from _Daniel Suteu_, Apr 09 2022