A356833 - OEIS

%I #50 Nov 02 2022 07:51:34

%S 5,13,19,31,37,43,53,61,67,73,79,83,89,103,109,127,131,139,151,157,

%T 163,173,181,193,199,211,223,233,241,251,257,263,269,271,277,293,307,

%U 311,313,317,331,337,353,367,373,379,383,389,397,401,409,421,433,443,449,457,461,463,467,479

%N Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a square.

%e 13 is a term because up to the next prime 17, tau(14) = 4, tau(15) = 4, tau(16) = 5, thus the smallest tau(k) is 4 and 4 is a square (2^2).

%e 23 is prime but not a term because up to the next prime 29, tau(24) = 8, tau(25) = 3, tau(26) = 4, tau(27) = 4, tau(28) = 6, thus the smallest tau(k) = 3 and 3 is not a square.

%o (PARI) isok(p)=issquare(vecmin(apply(numdiv, [p+1..nextprime(p+1)-1])));

%o forprime(p=3, 2000, if(isok(p), print1(p", ")))

%Y Cf. A000005, A000040, A000290, A061112, A036436.

%Y Cf. A353284, A353285, A353286, A357170, A357175.

%K nonn,easy

%O 1,1

%A _Claude H. R. Dequatre_, Sep 16 2022