OFFSET
1,4
COMMENTS
Conjecture: a(n) > 0 for all n > 1.
This is a refinement of part (i) of the conjecture in A238165.
We have verified the conjecture for n up to 21500.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..2900
Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014
EXAMPLE
a(18) = 1 since 6 == 1 (mod 1), and pi(1*18) = 7 divides pi(6*18) = 28.
a(50) = 1 since 7 == 1 (mod 3), and pi(3*50) = 35 divides pi(7*50) = 70.
a(379) = 1 since 353 == 1 (mod 4), and pi(4*379) = 240 divides pi(353*379) = 12480.
MATHEMATICA
m[k_, j_, n_]:=Mod[PrimePi[k*n], PrimePi[j*n]]==0
a[n_]:=Sum[If[m[j*q+1, j, n], 1, 0], {j, 1, n-1}, {q, 1, (n-1)/j}]
Table[a[n], {n, 1, 80}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Feb 20 2014
STATUS
approved