

A237612


Least positive integer k such that A000720(k*n) is a square, or 0 if such a number k does not exist.


9



1, 1, 3, 2, 2, 4, 1, 1, 1, 1, 5, 2, 2, 2, 28, 34, 9, 3, 3, 5, 20, 7, 1, 1, 1, 1, 1, 1, 2, 14, 5, 17, 3, 16, 12, 23, 18, 4, 4, 30, 46, 10, 50, 23, 36, 18, 40, 14, 2, 2, 3, 3, 1, 1, 1, 1, 1, 1, 32, 7, 11, 68, 19, 79, 29, 267, 10, 8, 12, 6
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OFFSET

1,3


COMMENTS

According to the conjecture in A237598, we should always have 0 < a(n) < prime(n).


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000
Z.W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014


EXAMPLE

a(3) = 3 since A000720(3*3) = 4 is a square, but neither A000720(1*3) = 2 nor A000720(2*3) = 3 is a square.


MATHEMATICA

sq[n_]:=IntegerQ[Sqrt[PrimePi[n]]]
Do[Do[If[sq[k*n], Print[n, " ", k]; Goto[aa]], {k, 1, Prime[n]1}];
Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 100}]


CROSSREFS

Cf. A000290, A000720, A237578, A237597, A237598, A237614.
Sequence in context: A117643 A164522 A141862 * A111739 A182214 A216161
Adjacent sequences: A237609 A237610 A237611 * A237613 A237614 A237615


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Feb 10 2014


STATUS

approved



