A281294 Refactorable numbers k such that 2*k + 1 is also a refactorable number.

3280, 6160, 8320, 51520, 99904, 174640, 386320, 541840, 883120, 1690960, 2062480, 2365312, 2688880, 2959744, 3077680, 3152560, 3274240, 5375920, 6885760, 8925312, 10030720, 11219584, 11912080, 12058960, 14370160, 15854080, 18966640, 21839440, 22038160, 24787840, 26725360

Offset: 1

Author

Altug Alkan, Jan 19 2017

Keywords

• nonn

Comments

If k is in this sequence, then 2*k + 1 must be a square. So this sequence is a subsequence of A046092.

Examples

			3280 is a term because 3280 = 2^4 * 5 * 41 is divisible by d(3280) = 2^2 * 5 and 2 * 3280 + 1 = 3^8 is divisible by d(3^8) = 9.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033950, A036896, A046092.

Programs

Mathematica

Select[Table[2 n (n + 1), {n, 10^4}], Times @@ Boole@ Thread[Divisible[#, DivisorSigma[0, #]] &@ {#, 2 # + 1}] > 0 &] (* Michael De Vlieger, Jan 19 2017 *)

PARI

isA033950(n) = n % numdiv(n)== 0;
is(n) = isA033950(n) && isA033950(2*n+1);