A349496 Numbers of the form 4*t^2-2 (A060626) when t >= 1 is an integer that is not a term in A001542.

2, 34, 62, 98, 142, 194, 254, 322, 398, 482, 674, 782, 898, 1022, 1154, 1294, 1442, 1598, 1762, 1934, 2114, 2302, 2498, 2702, 2914, 3134, 3362, 3598, 3842, 4094, 4354, 4622, 4898, 5182, 5474, 5774, 6082, 6398, 6722, 7054, 7394, 7742, 8098, 8462, 8834, 9214, 9602, 9998, 10402

Offset: 1

Author

Bernard Schott, Nov 21 2021

Keywords

• nonn

Comments

Equivalently: numbers k for which there exists only one integer m with here m = k/2 + 1 such that A000178(k) / m! is a square, where A000178(k) = k$ = 1!*2!*...*k! is the superfactorial of k.

Examples

			A060626(3) = 34 and 3 is not a term in A001542; also 34$ / 18! is a square, hence 34 is a term.
		

Links

• Rick Mabry and Laura McCormick, Square products of punctured sequences of factorials, Gaz. Aust. Math. Soc., 2009, pages 346-352 (FFF 2. (3) p. 348).

Crossrefs

Cf. A000178, A001542, A348692, A349079.

Subsequence of A060626 and of A349080.

Programs

PARI

isok(m) = my(x=(m+2)/4, y); issquare(x, &y) && (denominator(y)==1) && !issquare(2*x+1); \\ Michel Marcus, Nov 22 2021