A237612 - OEIS

A237612

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

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

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: A327661 A117643 A141862 * A362465 A111739 A376310

Adjacent sequences: A237609 A237610 A237611 * A237613 A237614 A237615

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Feb 10 2014

STATUS

approved