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 1-4 of 4 results.

A078547 a(n) = lcm(n, A052429(n)) - n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 14, 0, 32, 102, 54, 152, 0, 21, 0, 115, 0, 25, 52, 351, 28, 493, 0, 62, 64, 0, 170, 70, 0, 740, 418, 78, 0, 123, 42, 473, 0, 135, 230, 1269, 0, 1715, 0, 204, 208, 742, 486, 0, 784, 1938, 1102, 2596, 0, 305, 124, 63, 128, 325, 0
Offset: 1

Views

Author

Labos Elemer, Dec 05 2002

Keywords

Comments

a(n)=0 if n is divisible by each nonzero digit, i.e., if n in A002796.

Crossrefs

Cf. A052429, A078546, A078548, A002796.

Programs

  • Mathematica
    lc[x_] := Apply[LCM, DeleteCases[IntegerDigits[x], 0]] Table[LCM[lc[w], w]-w, {w, 1, 128}]
  • PARI
    lcnzd(n) = lcm(select(x->(x!=0), digits(n)));
a(n) = lcm(n, lcnzd(n)) - n; \\ Michel Marcus, Mar 18 2018

A078548 a(n) = lcm(n, A052429(n)) - A052429(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 10, 36, 24, 10, 42, 112, 64, 162, 18, 40, 20, 132, 20, 40, 72, 364, 48, 504, 27, 90, 90, 30, 192, 90, 30, 756, 432, 108, 36, 160, 80, 504, 40, 160, 264, 1288, 40, 1728, 45, 250, 250, 780, 520, 50, 810, 1960, 1120, 2610, 54, 360, 180
Offset: 1

Views

Author

Labos Elemer, Dec 05 2002

Keywords

Crossrefs

Cf. A052429, A078546, A078547, A002796.

Programs

  • Mathematica
    lc[x_] := Apply[LCM, DeleteCases[IntegerDigits[x], 0]] Table[LCM[lc[w], w]-lc[w], {w, 1, 128}]
  • PARI
    lcnzd(n) = lcm(select(x->(x!=0), digits(n)));
a(n) = my(lc=lcnzd(n)); lcm(n, lc) - lc; \\ Michel Marcus, Mar 18 2018

A078546 LCM of n and its nonzero decimal digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 39, 28, 15, 48, 119, 72, 171, 20, 42, 22, 138, 24, 50, 78, 378, 56, 522, 30, 93, 96, 33, 204, 105, 36, 777, 456, 117, 40, 164, 84, 516, 44, 180, 276, 1316, 48, 1764, 50, 255, 260, 795, 540, 55, 840, 1995, 1160, 2655, 60, 366, 186
Offset: 1

Views

Author

Labos Elemer, Dec 05 2002

Keywords

Examples

			n=13: lcm(13,1,3) = 39 = a(13); a(x)=x if x is divisible by each nonzero digits, i.e., if x in A002796.

Crossrefs

Cf. A052429, A078547, A078548, A002796.

Programs

  • Mathematica
    lc[x_] := Apply[LCM, DeleteCases[IntegerDigits[x], 0]] Table[LCM[lc[w], w], {w, 1, 128}] NOT
  • PARI
    lcnzd(n) = lcm(select(x->(x!=0), digits(n)));
a(n) = lcm(n, lcnzd(n)); \\ Michel Marcus, Mar 18 2018

Formula

a(n) = lcm(n, A052429(n)).

A343504 a(n) is the least common multiple of the nonzero digits in factorial base expansion of n.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 6, 6, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 6, 6, 3, 3, 3, 3, 6, 6, 6, 6, 6
Offset: 0

Views

Author

Rémy Sigrist, Apr 17 2021

Keywords

Comments

a(0) = 1 by convention.

Examples

			For n = 1000000:
- the factorial base expansion of 1000000 is "2, 6, 6, 2, 5, 1, 2, 2, 0",
- so a(1000000) = lcm(1, 2, 5, 6) = 30.

Links

Crossrefs

Cf. A052429, A059590, A108731, A328582.

Programs

  • PARI
    a(n) = { my (v=1); for (r=2, oo, if (n==0, return (v), n%r, v=lcm(v, n%r)); n\=r) }

Formula

a(n) = 1 iff n belongs to A059590.
Showing 1-4 of 4 results.

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