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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A033950, A036896, A046092.

Sequence in context: A309284 A015326 A252074 * A043472 A203859 A107536

Adjacent sequences: A281291 A281292 A281293 * A281295 A281296 A281297

Keyword

nonn

Author

Altug Alkan, Jan 19 2017

Status

approved