login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A265578 LCM-transform of number of divisors function (A000005). 2
1, 2, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Terms larger than one occur at n = 2, 4, 6, 16, 24, 36, 64, 120, 840, 900, 1296, 7560, 44100, 46656, 83160, ... - Antti Karttunen, Nov 06 2018

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

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.

Antti Karttunen, Data supplement: n, a(n) computed for n =  1..100000

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;

with(numtheory);

t1:=[seq(tau(n), n=1..100)];

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]];

LCMXfm[Table[DivisorSigma[0, n], {n, 1, 100}]] (* Jean-Fran├žois Alcover, Dec 05 2017, from Maple *)

PROG

(PARI)

up_to = 16384;

LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2, len, g[n] = lcm(g[n-1], v[n]); b[n] = g[n]/g[n-1]); (b); };

v265578 = LCMtransform(vector(up_to, i, numdiv(i)));

A265578(n) = v265578[n]; \\ Antti Karttunen, Nov 06 2018

CROSSREFS

Cf. A000005.

Other LCM-transforms are A061446, A265574, A265575, A265576, A265577.

Sequence in context: A123864 A035175 A092412 * A279288 A078734 A028293

Adjacent sequences:  A265575 A265576 A265577 * A265579 A265580 A265581

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 02 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 7 13:59 EDT 2020. Contains 335495 sequences. (Running on oeis4.)