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 1-3 of 3 results.

A269223 Factorial of the sum of digits of n in base 3.

Original entry on oeis.org

1, 1, 2, 1, 2, 6, 2, 6, 24, 1, 2, 6, 2, 6, 24, 6, 24, 120, 2, 6, 24, 6, 24, 120, 24, 120, 720, 1, 2, 6, 2, 6, 24, 6, 24, 120, 2, 6, 24, 6, 24, 120, 24, 120, 720, 6, 24, 120, 24, 120, 720, 120, 720, 5040, 2, 6, 24, 6, 24, 120, 24, 120, 720, 6, 24, 120, 24, 120, 720, 120, 720
Offset: 0

Views

Author

M. F. Hasler, Mar 15 2016

Keywords

Comments

Sequence A093659 is the binary (base 2) and sequence A269221 is the decimal (base 10) version.

Crossrefs

Cf. A000142, A053735, A166350, A093659.

Programs

  • Mathematica
    Table[Total[IntegerDigits[n, 3]]!, {n, 0, 70}] (* Michael De Vlieger, Mar 15 2016 *)
  • PARI
    A269223(n)=sumdigits(n,3)! \\ sumdigits(.,3) requires version > 2.7.1; see A053735 for a substitute.
  • PARI
    a(n) = vecsum(digits(n,3))!; \\ Michel Marcus, Mar 15 2016

Formula

a(n) = A000142(A053735(n)).

A269224 Factorial of the sum of digits of n in base 4.

Original entry on oeis.org

1, 1, 2, 6, 1, 2, 6, 24, 2, 6, 24, 120, 6, 24, 120, 720, 1, 2, 6, 24, 2, 6, 24, 120, 6, 24, 120, 720, 24, 120, 720, 5040, 2, 6, 24, 120, 6, 24, 120, 720, 24, 120, 720, 5040, 120, 720, 5040, 40320, 6, 24, 120, 720, 24, 120, 720, 5040, 120, 720, 5040, 40320, 720, 5040, 40320
Offset: 0

Views

Author

M. F. Hasler, Mar 15 2016

Keywords

Comments

See sequences A093659, A269223 and A269221 for the base 2, base 3 and base 10 analog.

Crossrefs

Cf. A000142, A053737, A166350, A093659, A269223, A269221.

Programs

  • Mathematica
    Table[Total[IntegerDigits[n, 4]]!, {n, 0, 62}] (* Michael De Vlieger, Mar 15 2016 *)
  • PARI
    A269224(n)=sumdigits(n,4)! \\ sumdigits(.,4) requires version >= 2.7; see A053737 for a substitute.
  • PARI
    a(n) = vecsum(digits(n,4))!; \\ Michel Marcus, Mar 15 2016

Formula

a(n) = A000142(A053737(n)).

A384955 a(n) is the multinomial coefficient of the digits of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1, 6, 21, 56, 126, 252, 462, 792, 1287, 2002, 1, 7, 28, 84, 210, 462, 924, 1716, 3003, 5005
Offset: 0

Views

Author

Stefano Spezia, Jun 13 2025

Keywords

Examples

			a(35) = (3+5)!/(3!*5!) = 40320/(6*120) = 56;
a(1512) = (1+5+1+2)!/(1!*5!*1!*2!) = 362880/(120*2) = 1512.

Links

Crossrefs

Cf. A037124, A066459, A093659, A269221.

Programs

  • Maple
    a:= n-> (l-> combinat[multinomial](add(i,i=l), l[]))(convert(n, base, 10)):
seq(a(n), n=0..69);  # Alois P. Heinz, Jun 15 2025
  • Mathematica
    a[n_]:=Multinomial @@IntegerDigits[n]; Array[a,70,0]
  • Python
    from math import factorial, prod
def a(n): return factorial(sum(digits:=list(map(int, str(n))))) // prod(factorial(x) for x in digits)
print([a(n) for n in range(70)]) # David Radcliffe, Jun 15 2025

Formula

a(n) = A269221(n)/A066459(n).
a(n) = 1 iff n is equal to 0 or has only one nonzero digit (cf. A037124).
Conjecture: a(n) = n iff n = 1 or n = 1512.
Showing 1-3 of 3 results.

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

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