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%I #20 Nov 02 2022 07:52:34
%S 29,41,101,137,229,281,349,439,617,641,643,739,821,823,853,967,1087,
%T 1423,1429,1447,1549,1579,1597,1693,1697,1783,1877,1999,2081,2131,
%U 2237,2239,2293,2377,2381,2539,2617,2657,2683,2693,2713,2749,2791,2801,3079,3319
%N Primes p such that the minimum of the number of divisors among the numbers between p and NextPrime(p) is a cube.
%e 349 is a term because up to the next prime 353, tau(350) = 12, tau(351) = 8, tau(352) = 12, thus the smallest tau(k) = 8 and 8 is a cube (2^3).
%e 379 is prime but not a term because up to the next prime 383, tau(380) = 12, tau(381) = 4, tau(382) = 4, thus the smallest tau(k) is 4 and 4 is not a cube.
%o (PARI) isok(p)=ispower(vecmin(apply(numdiv, [p+1..nextprime(p+1)-1])), 3);
%o forprime(p=3, 10000, if(isok(p), print1(p", ")))
%Y Cf. A000005, A000040, A000578. A061112.
%Y Cf. A353284, A353285, A353286, A356833, A357170.
%K nonn,easy
%O 1,1
%A _Claude H. R. Dequatre_, Sep 16 2022