A237612 - OEIS

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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.

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]]]