OFFSET
1,3
COMMENTS
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..900
Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014.
EXAMPLE
a(4) = 1 since 3 is prime and there are exactly 3 squarefree numbers among 1, ..., (3-1)/2*4 (namely, 1, 2, 3).
a(14) = 1 since 5 and 17 are both prime, and there are exactly 17 squarefree numbers among 1, ..., (5-1)/2*14.
a(19) = 1 since 3 and 13 are both prime, and there are exactly 13 squarefree numbers among 1, ..., (3-1)/2*19 (namely, 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19).
a(29) = 1 since 41 and 353 are both prime, and there are exactly 353 squarefree numbers among 1, ..., (41-1)/2*29 = 580.
MATHEMATICA
s[n_]:=Sum[If[SquareFreeQ[k], 1, 0], {k, 1, n}]
a[n_]:=Sum[If[PrimeQ[s[(Prime[k]-1)/2*n]], 1, 0], {k, 2, PrimePi[2n-1]}]
Table[a[n], {n, 1, 80}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Mar 02 2014
STATUS
approved