A336823 -id:A336823 - cp's OEIS frontend

A326889 a(1) = 1; thereafter a(n) = a(n-1) / phi(n) if phi(n) divides a(n-1), otherwise a(n) = a(n-1) * phi(n), where phi is the Euler phi-function A000010.

1, 1, 2, 1, 4, 2, 12, 3, 18, 72, 720, 180, 15, 90, 720, 90, 1440, 240, 4320, 540, 45, 450, 9900, 79200, 3960, 330, 5940, 495, 13860, 110880, 3696, 231, 4620, 73920, 3080, 36960, 1330560, 73920, 3080, 49280, 1232, 14784, 352, 7040, 168960, 7680, 353280, 22080

Offset: 1

Rémy Sigrist, Sep 13 2019

nonn

This sequence has similarities with A008336 and with A008338.

			The first terms, alongside phi(n), are:
  n   a(n)  phi(n)
  --  ----  ------
   1     1       1
   2     1       1
   3     2       2
   4     1       2
   5     4       4
   6     2       2
   7    12       6
   8     3       4
   9    18       6
  10    72       4

Rémy Sigrist, Table of n, a(n) for n = 1..2500

See A327442 for an additive variant.

Cf. A000010, A008336, A008338, A336823.

for (n=1, 48, print1 (v=if (n==1, 1, v%e=eulerphi(n), v*e, v/e) ", "))

A337643 a(1) = 1; thereafter a(n) = a(n-1) / lpf(n) if lpf(n) divides a(n-1), otherwise a(n) = a(n-1) * lpf(n), where lpf is the least prime factor function A020639.

Original entry on oeis.org

1, 1, 2, 6, 3, 15, 30, 210, 105, 35, 70, 770, 385, 5005, 10010, 30030, 15015, 255255, 510510, 9699690, 4849845, 1616615, 3233230, 74364290, 37182145, 7436429, 14872858, 44618574, 22309287, 646969323, 1293938646, 40112098026, 20056049013, 6685349671, 13370699342

Offset: 1

N. J. A. Sloane, Sep 21 2020

nonn

Cf. A020639, A326889, A327442, A336823.

A020639 := proc(n) if n = 1 then 1; else min(op(numtheory[factorset](n))) ; end if; end proc:
a:=[1]; t:=1;
for n from 2 to 50 do
u:=A020639(n-1);
if (t mod u) = 0 then t:=t/u else t:=t*u; fi; a:=[op(a),t];
od;
a;

cp's OEIS Frontend

A326889 a(1) = 1; thereafter a(n) = a(n-1) / phi(n) if phi(n) divides a(n-1), otherwise a(n) = a(n-1) * phi(n), where phi is the Euler phi-function A000010.

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