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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)