A265576 LCM-transform of EKG sequence A064413.

1, 2, 2, 3, 1, 3, 1, 2, 5, 1, 1, 1, 7, 1, 1, 1, 2, 1, 11, 1, 1, 3, 1, 5, 1, 1, 13, 1, 1, 1, 2, 17, 1, 1, 1, 19, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 29, 1, 1, 1, 31, 1, 1, 1, 2, 1, 37, 1, 1, 1, 1, 1, 1, 41

Offset

1,2

Comments

This is not equal to A014963(A064413(n)) because the EKG-permutation doesn't satisfy the property that all prime powers should appear before any of their multiples, as, for example, A064413(4) = 6 comes before A064413(5) = 3. See comments in A368900. - Antti Karttunen, Jan 13 2024

Links

Table of n, a(n) for n=1..73.

A. Nowicki, Strong divisibility and LCM-sequences, arXiv:1310.2416 [math.NT], 2013.

A. Nowicki, Strong divisibility and LCM-sequences, Am. Math. Mnthly 122 (2015), 958-966.

Maple

LCMXfm:=proc(a) local L, i, n, g, b;
L:=nops(a);
g:=Array(1..L, 0); b:=Array(1..L, 0);
b[1]:=a[1]; g[1]:=a[1];
for n from 2 to L do g[n]:=ilcm(g[n-1], a[n]); b[n]:=g[n]/g[n-1]; od;
lprint([seq(b[i], i=1..L)]);
end;
# let t1 contain the first 100 terms of A064413
LCMXfm(t1);

Mathematica

LCMXfm[a_List] := Module[{L = Length[a], b, g}, b[1] = g[1] = a[[1]]; b[_] = 0; g[_] = 0; Do[g[n] = LCM[g[n - 1], a[[n]]]; b[n] = g[n]/g[n - 1], {n, 2, L}]; Array[b, L]];
ekg[1] = 1; ekg[2] = 2; ekg[n_] := ekg[n] = For[k = 1, True, k++, If[FreeQ[ Array[ekg, n - 1], k] && !CoprimeQ[k, ekg[n - 1]], Return[k]]];
LCMXfm[Array[ekg, 100]] (* Jean-François Alcover, Dec 05 2017 *)

Crossrefs

Cf. A064413.

Other LCM-transforms are A014963, A061446, A265574, A265575, A368900 (see the last one for many other examples).

Sequence in context: A274528 A166248 A180257 * A083040 A083899 A339461

Adjacent sequences: A265573 A265574 A265575 * A265577 A265578 A265579

Keyword

nonn

Author

N. J. A. Sloane, Jan 02 2016

Status

approved