A320002 a(0) = 1; for n > 0, a(n) = A002828(n) * a(n-A002828(n)), where A002828(n) is the least number of squares that add up to n.

1, 1, 2, 3, 3, 6, 9, 12, 18, 18, 36, 54, 54, 108, 162, 216, 216, 432, 432, 648, 864, 1296, 1944, 2592, 3888, 3888, 7776, 11664, 15552, 23328, 34992, 46656, 69984, 104976, 139968, 209952, 209952, 419904, 629856, 839808, 1259712, 1679616, 2519424, 3779136, 5038848, 7558272, 11337408, 15116544, 22674816, 22674816, 45349632

Offset

0,3

Comments

Product of A002828(x) computed over all x encountered when map x -> x - A002828(x) is iterated, starting from x = n, until 0 is reached.

Sequence is monotonic because A255131 is monotonic.

All terms are 3-smooth (A003586).

Links

Antti Karttunen, Table of n, a(n) for n = 0..121

Formula

a(0) = 1; for n > 0, a(n) = A002828(n) * a(n-A002828(n)).

Mathematica

Nest[Append[#1, #2 #1[[-#2]] ] & @@ {#, If[First@ # > 0, 1, Length@ First@ Split@ # + 1] &@ SquaresR[Range@ 4, Length@ #]} &, {1}, 50] (* Michael De Vlieger, Nov 25 2018, after Harvey P. Dale at A002828 *)

Prog

(PARI)
istwo(n:int) = { my(f); if(n<3, return(n>=0); ); f=factor(n>>valuation(n, 2)); for(i=1, #f[, 1], if(bitand(f[i, 2], 1)==1&&bitand(f[i, 1], 3)==3, return(0))); 1 };
isthree(n:int) = { my(tmp=valuation(n, 2)); bitand(tmp, 1)||bitand(n>>tmp, 7)!=7 };
A002828(n) = if(issquare(n), !!n, if(istwo(n), 2, 4-isthree(n))); \\ From A002828
A255131(n) = (n-A002828(n));
A320002(n) = { my(m=1, v); while(n>0, v = A002828(n); m *= v; n -= v); (m); };
(PARI) A320002(n) = if(0==n, 1, A002828(n)*A320002(n-A002828(n)));

Crossrefs

Cf. A002828, A003586, A255131, A276573.

Cf. also A320008, A320009.

Sequence in context: A276096 A074717 A218137 * A129068 A079888 A165257

Adjacent sequences: A319999 A320000 A320001 * A320003 A320004 A320005

Keyword

nonn

Author

Antti Karttunen, Nov 24 2018

Status

approved