A102442 Number of iterations needed to transform n by A102440 into a 3-smooth number.

0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 1, 2, 3, 0, 1, 2, 0, 1, 3, 1, 3, 0, 2, 2, 1, 0, 2, 2, 2, 1, 3, 1, 3, 2, 1, 3, 4, 0, 1, 1, 2, 2, 3, 0, 2, 1, 2, 3, 4, 1, 4, 3, 1, 0, 2, 2, 3, 2, 3, 1, 4, 0, 4, 2, 1, 2, 2, 2, 3, 1, 0, 3, 4, 1, 2, 3, 3, 2, 4, 1, 2, 3, 3, 4, 2, 0, 3, 1, 2, 1, 3, 2, 3, 2, 1

Offset

1,11

Links

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

Formula

a(n) = 0 iff n is 3-smooth (A003586);

a(A102444(n)) = n and a(m) < n for m < a(A102444(n)).

Example

A102440(A102440(A102440(41))) = 24 and A102440(24) = 24:
41 -> 3*13 -> 3*[13->2*5] = 2*3*5 -> 2*3*[5->2*2] = 3*2^3 = 24,
therefore a(41) = 3, A102443(41) = 24.

Mathematica

g[p_] := g[p] = For[k = p - 1, True, k--, If[PrimeOmega[k] == 2, Return[k]]]; f[n_] := Product[{p, e} = pe; If[p <= 3, p, g[p]]^e, {pe, FactorInteger[n]}]; a[n_] := -1 + Length @ NestWhileList[f, n, FactorInteger[#][[-1, 1]] > 3 &]; Array[a, 105] (* Amiram Eldar, Feb 04 2020 after Jean-François Alcover at A102440 *)

Crossrefs

Cf. A003586, A102440, A102443, A102444.

Sequence in context: A133701 A230417 A287263 * A091182 A001822 A351380

Adjacent sequences: A102439 A102440 A102441 * A102443 A102444 A102445

Keyword

nonn

Author

Reinhard Zumkeller, Jan 09 2005

Status

approved