A320008 -id:A320008 - cp's OEIS frontend

A320009 a(0) = 1; for n > 0, a(n) = A000005(n) * a(n-A000005(n)), where A000005(n) gives the number of divisors of n.

1, 1, 2, 2, 3, 4, 8, 8, 12, 24, 32, 48, 48, 96, 128, 192, 240, 384, 288, 768, 768, 1536, 1152, 3072, 1920, 3456, 4608, 12288, 6912, 24576, 9216, 49152, 27648, 98304, 36864, 196608, 110592, 393216, 147456, 786432, 221184, 1572864, 294912, 3145728, 884736, 4718592, 1179648, 9437184, 1474560, 3538944, 5308416, 37748736, 7077888, 75497472

Offset: 0

Antti Karttunen, Nov 24 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 0..150

Cf. A000005, A049820, A259934.

Cf. also A320002, A320008, A320016.

Nest[Append[#1, #2 #1[[-#2]] ] & @@ {#, DivisorSigma[0, Length@ #]} &, {1}, 53] (* Michael De Vlieger, Nov 25 2018 *)

A320009(n) = if(0==n,1,numdiv(n)*A320009(n-numdiv(n)));

a(0) = 1; for n > 0, a(n) = A000005(n) * a(n-A000005(n)).

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.

Original entry on oeis.org

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

Antti Karttunen, Nov 24 2018

nonn

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).

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

Cf. A002828, A003586, A255131, A276573.

Cf. also A320008, A320009.

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 *)

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); };

A320002(n) = if(0==n,1,A002828(n)*A320002(n-A002828(n)));

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

cp's OEIS Frontend

A320009 a(0) = 1; for n > 0, a(n) = A000005(n) * a(n-A000005(n)), where A000005(n) gives the number of divisors of n.

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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.

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