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A357170
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Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a prime power.
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3
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3, 5, 7, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 73, 79, 83, 89, 101, 103, 109, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 181, 193, 199, 211, 223, 229, 233, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 349, 353, 359, 367, 373
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OFFSET
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1,1
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LINKS
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EXAMPLE
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19 is a term because up to the next prime 23, tau(20) = 6, tau(21) = 4, tau(22) = 4, thus the smallest tau(k) is 4 and 4 is a prime power (2^2).
97 is prime but not a term because up to the next prime 101, tau(98) = 6, tau(99) = 6, tau(100) = 9, thus the smallest tau(k) is 6 and 6 is not a prime power.
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PROG
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(PARI) isok(p)=isprimepower(vecmin(apply(numdiv, [p+1..nextprime(p+1)-1])));
forprime(p=3, 2000, if(isok(p), print1(p", ")))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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