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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Zhi-Wei 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

Zhi-Wei Sun, Feb 10 2014

STATUS

approved

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Last modified March 24 11:49 EDT 2019. Contains 321448 sequences. (Running on oeis4.)