cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A327443 Indices of zeros in A327442.

Original entry on oeis.org

0, 2, 4, 13, 145, 416, 621, 1856, 4730, 5163, 8113, 18260, 142396, 1650399, 6569927, 19975865, 23773865, 371728346, 517406582, 642281555, 864490611, 1352215149, 1503350552
Offset: 1

Views

Author

N. J. A. Sloane, Sep 12 2019

Keywords

Crossrefs

Cf. A327442.

Extensions

a(12)-a(20) from Rémy Sigrist, Sep 13 2019
a(21)-a(23) from Seiichi Manyama, Sep 13 2019

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.

Original entry on oeis.org

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

Views

Author

Rémy Sigrist, Sep 13 2019

Keywords

Comments

This sequence has similarities with A008336 and with A008338.

Examples

			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

Links

Crossrefs

See A327442 for an additive variant.
Cf. A000010, A008336, A008338, A336823.

Programs

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

A330725 a(0) = 0; thereafter a(n) = a(n-1) + sigma(n) if sigma(n) > a(n-1), otherwise a(n) = a(n-1) - sigma(n), where sigma is the sum of divisors function A000203.

Original entry on oeis.org

0, 1, 4, 0, 7, 1, 13, 5, 20, 7, 25, 13, 41, 27, 3, 27, 58, 40, 1, 21, 63, 31, 67, 43, 103, 72, 30, 70, 14, 44, 116, 84, 21, 69, 15, 63, 154, 116, 56, 0, 90, 48, 144, 100, 16, 94, 22, 70, 194, 137, 44, 116, 18, 72, 192, 120, 0, 80, 170, 110, 278, 216, 120, 16
Offset: 0

Views

Author

Alois P. Heinz, Jan 11 2020

Keywords

Links

Crossrefs

Cf. A000203, A008344, A008345, A008348, A076042, A111466, A126646, A327442, A331165.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n=0, 0, ((s, t)-> s+
      `if`(s
  • Mathematica
    nxt[{n_,a_}]:={n+1,If[DivisorSigma[1,n+1]>a,a+DivisorSigma[1,n+1],a- DivisorSigma[ 1,n+1]]}; NestList[nxt,{0,0},70][[All,2]] (* Harvey P. Dale, May 14 2022 *)

A331165 a(n) = a(n-1) + p(n) if p(n) > a(n-1), otherwise a(n) = a(n-1) - p(n), where p is the partition function A000041 (assuming a(n) = 0 for n < 0).

Original entry on oeis.org

1, 0, 2, 5, 0, 7, 18, 3, 25, 55, 13, 69, 146, 45, 180, 4, 235, 532, 147, 637, 10, 802, 1804, 549, 2124, 166, 2602, 5612, 1894, 6459, 855, 7697, 16046, 5903, 18213, 3330, 21307, 42944, 16929, 48114, 10776, 55359, 2185, 65446, 140621, 51487, 157045, 32291, 179564
Offset: 0

Views

Author

Alois P. Heinz, Jan 11 2020

Keywords

Links

Crossrefs

Cf. A000041, A008344, A008345, A008348, A076042, A111466, A126646, A327442, A330725.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n<0, 0, ((s, t)-> s+
     `if`(s
  • Mathematica
    a[n_] := a[n] = If[n<0, 0, With[{a1 = a[n-1], p = PartitionsP[n]}, If[p>a1, a1 + p, a1 - p]]];
a /@ Range[0, 70] (* Jean-François Alcover, Jan 05 2021 *)
  • PARI
    lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, my(p = numbpart(n-1)); va[n] = va[n-1] - p; if (va[n] < 0, va[n] += 2*p);); va;} \\ Michel Marcus, Jan 06 2021

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

Views

Author

N. J. A. Sloane, Sep 21 2020

Keywords

Crossrefs

Cf. A020639, A326889, A327442, A336823.

Programs

  • Maple
    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;
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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