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A061399
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Number of nonsquarefree integers between primes prime(n) and prime(n+1).
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12
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0, 1, 0, 2, 1, 1, 1, 1, 4, 0, 2, 1, 0, 2, 4, 2, 1, 2, 1, 1, 2, 2, 2, 3, 3, 0, 1, 1, 1, 7, 1, 3, 0, 4, 1, 3, 2, 1, 4, 2, 1, 3, 1, 1, 1, 4, 3, 2, 1, 1, 2, 1, 6, 2, 2, 2, 1, 3, 2, 0, 4, 6, 1, 1, 2, 4, 3, 5, 1, 3, 1, 4, 3, 3, 1, 3, 2, 1, 3, 3, 1, 4, 1, 1, 2, 2, 3, 2, 0, 1, 5, 3, 2, 3, 1, 3, 4, 1, 9, 1, 5, 2, 3, 0, 3
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OFFSET
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1,4
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LINKS
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EXAMPLE
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Between 113 and 127 the 7 numbers which are not squarefree are {116,117,120,121,124,125,126}, so a(30)=7.
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MATHEMATICA
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Count[Range[#[[1]]+1, #[[2]]-1], _?(!SquareFreeQ[#]&)]&/@Partition[Prime[Range[120]], 2, 1] (* Harvey P. Dale, Mar 31 2024 *)
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PROG
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(PARI) { n=0; q=2; forprime (p=3, prime(1001), a=0; for (i=q+1, p-1, a+=!issquarefree(i)); write("b061399.txt", n++, " ", a); q=p ) } \\ Harry J. Smith, Jul 22 2009
(Python)
from sympy import mobius, prime
def A061399(n): return sum(not mobius(m) for m in range(prime(n)+1, prime(n+1))) # Chai Wah Wu, Jul 20 2024
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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