A357175 Primes p such that the minimum of the number of divisors among the numbers between p and NextPrime(p) is a cube.

29, 41, 101, 137, 229, 281, 349, 439, 617, 641, 643, 739, 821, 823, 853, 967, 1087, 1423, 1429, 1447, 1549, 1579, 1597, 1693, 1697, 1783, 1877, 1999, 2081, 2131, 2237, 2239, 2293, 2377, 2381, 2539, 2617, 2657, 2683, 2693, 2713, 2749, 2791, 2801, 3079, 3319

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

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).
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.

Prog

(PARI) isok(p)=ispower(vecmin(apply(numdiv, [p+1..nextprime(p+1)-1])), 3);
forprime(p=3, 10000, if(isok(p), print1(p", ")))

Crossrefs

Cf. A000005, A000040, A000578. A061112.

Cf. A353284, A353285, A353286, A356833, A357170.

Sequence in context: A157257 A214405 A104072 * A070268 A139870 A173874

Adjacent sequences: A357172 A357173 A357174 * A357176 A357177 A357178

Keyword

nonn,easy

Author

Claude H. R. Dequatre, Sep 16 2022

Status

approved