A037124 -id:A037124 - cp's OEIS frontend

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

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

Stefano Spezia, Jun 13 2025

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

Stefano Spezia, Table of n, a(n) for n = 0..10000

Cf. A037124, A066459, A093659, A269221.

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

a[n_]:=Multinomial @@IntegerDigits[n]; Array[a,70,0]

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

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.

A071061 Abjad values of the Arabic letters in the traditional order for abjad calculations.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000

Offset: 1

Koksal Karakus (karakusk(AT)hotmail.com), May 26 2002

The Greek or Ionian numerals are similar, but omit 1000. - Charles R Greathouse IV, Jun 25 2012

F. Lewis, Overview of the abjad numerological system

Subsequence of A037124.

Cf. A051596.

A243079 Numbers n such that A = n - DigitProd(n) is divisible by the largest power of 10 <= A.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 35, 55, 62, 64, 66, 68, 75, 95, 236, 315, 324, 575, 612, 828, 935, 944, 4384, 5175, 7688, 7735, 8128, 8672, 9135, 9144, 9575, 91575

Offset: 1

Derek Orr, May 30 2014

Trivially numbers in A037124 satisfy this but are not contained in this sequence.

			35-3*5 = 20 is divisible by the highest power of 10 below it (10^1). So 20 is a member of this sequence.

Cf. A055642, A037124, A242948.

DP(n)={p=1; d=digits(n); for(i=1, #d, p*=d[i]); return(p)}
for(k=1,10^7,if(n%10!=0&&(n-DP(n))%(10^(#Str(n-DP(n))-1))==0,print1(n,", ")))

A380818 Numbers k such that the Diophantine equation d_rx^r + ... + d_0x^0 = 0 has an integer solution. k = (d_r .. d_0) in decimal notation, d_i are the digits of k.

Original entry on oeis.org

0, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 110, 120, 121, 130, 132, 140, 143, 144, 150, 154, 156, 160, 165, 168, 169, 170, 176, 180, 187, 190, 198, 200, 210, 220, 230, 231, 240, 242, 250

Offset: 1

Ctibor O. Zizka, Feb 04 2025

For r >= 1, d_r >= 1, numbers k = d_r*10^r are terms. It looks like the solution x (if it exists) is from [-9, 0].

			k = 68: the Diophantine equation 6*x + 8 = 0 has no integer solution, thus k = 68 is not a term.
k = 132: the Diophantine equation 1*x^2 + 3*x + 2 = 0 has integer solutions x = -1, x = -2, thus k = 132 is a term.

Cf. A037124 (for k >= 10).

cp's OEIS Frontend

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

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A071061 Abjad values of the Arabic letters in the traditional order for abjad calculations.

Views

Author

Keywords

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Links

Crossrefs

A243079 Numbers n such that A = n - DigitProd(n) is divisible by the largest power of 10 <= A.

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Author

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PARI

A380818 Numbers k such that the Diophantine equation d_rx^r + ... + d_0x^0 = 0 has an integer solution. k = (d_r .. d_0) in decimal notation, d_i are the digits of k.

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Author

Keywords

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cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Python

Formula

A071061 Abjad values of the Arabic letters in the traditional order for abjad calculations.

Views

Author

Keywords

Comments

Links

Crossrefs

A243079 Numbers n such that A = n - DigitProd(n) is divisible by the largest power of 10 <= A.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

A380818 Numbers k such that the Diophantine equation d_r*x^r + ... + d_0*x^0 = 0 has an integer solution. k = (d_r .. d_0) in decimal notation, d_i are the digits of k.

Views

Author

Keywords

Comments

Examples

Crossrefs

A380818 Numbers k such that the Diophantine equation d_rx^r + ... + d_0x^0 = 0 has an integer solution. k = (d_r .. d_0) in decimal notation, d_i are the digits of k.