A017643 a(n) = (12n+10)^3.

1000, 10648, 39304, 97336, 195112, 343000, 551368, 830584, 1191016, 1643032, 2197000, 2863288, 3652264, 4574296, 5639752, 6859000, 8242408, 9800344, 11543176, 13481272, 15625000, 17984728, 20570824, 23393656, 26463592, 29791000, 33386248, 37259704

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

6n + 5 = (12n + 10) / 2 is never a square, as 5 is not a quadratic residue modulo 6. Using this, we can show that each term has an even square part and an even squarefree part, neither part being a power of 2. (Less than 2% of integers have this property - see A339245.) - Peter Munn, Dec 14 2020

Links

• Eric Weisstein's World of Mathematics, Quadratic Residue.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

A000578, A017641 are used in a formula defining this sequence.

Subsequence of A339245.

Cf. A017642, A017644.

Programs

Maple

A017643:=(12*n+10)^3; seq(A017643(n), n=0..100); # Wesley Ivan Hurt, Nov 25 2013

Mathematica

(12Range[0,30]+10)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{1000,10648,39304,97336},30] (* Harvey P. Dale, Sep 30 2011 *)

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with a(0)=1000, a(1)=10648, a(2)=39304, a(3)=97336. [Harvey P. Dale, Sep 30 2011]

a(n) = A017641(n)^3 = A000578(A017641(n)). - Michel Marcus, Nov 25 2013