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 1-10 of 13 results. Next

A023837 Sum of exponents in prime-power factorization of C(5n,n).

Original entry on oeis.org

0, 1, 3, 3, 4, 6, 7, 8, 8, 7, 9, 12, 11, 14, 13, 14, 12, 15, 14, 15, 18, 17, 17, 19, 18, 17, 23, 22, 21, 25, 23, 26, 21, 23, 22, 24, 23, 24, 27, 27, 27, 27, 29, 27, 28, 31, 30, 33, 28, 31, 32, 33, 36, 38, 36, 38, 37, 35, 39, 40, 41, 41, 41, 39, 34, 38, 38, 38, 39, 41, 39, 46, 41, 43, 45, 43, 45, 48, 47
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A001449, A023838, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

  • Maple
    with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(binomial(5*n,n)) fi end: seq(a(n), n=0..78); # Zerinvary Lajos, Apr 11 2008
  • Mathematica
    Table[PrimeOmega[Binomial[5 n, n]], {n, 0, 78}] (* Ivan Neretin, Nov 08 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,n)); \\ Amiram Eldar, Jun 14 2025

Formula

a(n) = A001222(A001449(n)). - Amiram Eldar, Jun 14 2025

Extensions

Offset changed to 0 and a(0) prepended by Amiram Eldar, Jun 14 2025

A023839 Sum of exponents in prime-power factorization of C(5n,n-2).

Original entry on oeis.org

0, 2, 3, 5, 6, 7, 8, 9, 9, 10, 10, 13, 12, 15, 13, 15, 15, 14, 16, 18, 16, 18, 19, 19, 22, 23, 23, 24, 23, 23, 22, 26, 22, 24, 25, 24, 24, 28, 26, 27, 28, 27, 28, 33, 30, 29, 31, 33, 33, 34, 35, 38, 37, 39, 37, 37, 38, 38, 42, 40, 38, 40, 39, 41, 38, 36, 38, 43, 40, 44, 42, 44, 42, 44, 45, 48, 49, 49
Offset: 2

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A004344, A023837, A023838, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

  • Mathematica
    Table[PrimeOmega[Binomial[5 n, n - 2]], {n, 2, 79}] (* Ivan Neretin, Nov 08 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,n-2)); \\ Amiram Eldar, Jun 14 2025

Formula

From Amiram Eldar, Jun 14 2025: (Start)
a(n) = A001222(A004344(n-2)).
a(n) = A023838(n) - A001222(4*n+2) + A001222(n-1). (End)

Extensions

Offset corrected to 2 by Ivan Neretin, Nov 08 2017

A023840 Sum of exponents in prime-power factorization of C(5n,n-3).

Original entry on oeis.org

0, 3, 5, 5, 7, 8, 8, 11, 11, 10, 12, 14, 13, 14, 16, 16, 14, 18, 17, 17, 18, 18, 19, 25, 23, 23, 25, 24, 23, 24, 23, 26, 24, 24, 25, 26, 27, 27, 28, 29, 25, 30, 32, 31, 31, 30, 33, 36, 33, 37, 38, 38, 39, 40, 36, 40, 39, 39, 39, 41, 38, 39, 43, 42, 37, 38, 41, 42, 44, 43, 43, 45, 43, 46, 50, 48, 49
Offset: 3

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A004345, A023837, A023838, A023839, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

  • Mathematica
    Table[PrimeOmega[Binomial[5 n, n - 3]], {n, 3, 79}] (* Ivan Neretin, Nov 08 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,n-3)); \\ Amiram Eldar, Jun 14 2025

Formula

From Amiram Eldar, Jun 14 2025: (Start)
a(n) = A001222(A004345(n)).
a(n) = A023838(n) - A001222(4*n+3) + A001222(n-2). (End)

Extensions

Offset corrected to 3 by Ivan Neretin, Nov 08 2017

A023841 Sum of exponents in prime-power factorization of C(5n,n-4).

Original entry on oeis.org

0, 2, 3, 4, 5, 6, 9, 9, 9, 10, 11, 10, 12, 13, 15, 13, 15, 16, 15, 15, 16, 17, 21, 22, 22, 22, 24, 19, 21, 22, 23, 23, 23, 23, 24, 25, 25, 25, 28, 24, 26, 31, 29, 27, 29, 30, 33, 33, 36, 35, 36, 36, 37, 36, 39, 37, 38, 37, 37, 34, 36, 40, 42, 38, 36, 39, 40, 40, 42, 42, 41, 43, 43, 47, 48, 45, 46, 47
Offset: 4

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A004346, A023837, A023838, A023839, A023840, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

  • Mathematica
    Table[PrimeOmega[Binomial[5 n, n - 4]], {n, 4, 81}] (* Ivan Neretin, Nov 08 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,n-4)); \\ Amiram Eldar, Jun 14 2025

Formula

From Amiram Eldar, Jun 14 2025: (Start)
a(n) = A001222(A004346(n)).
a(n) = A023840(n) - A001222(4*n+4) + A001222(n-3). (End)

Extensions

Offset corrected to 4 by Ivan Neretin, Nov 08 2017

A023842 Sum of exponents in prime-power factorization of C(5n,n-5).

Original entry on oeis.org

0, 3, 3, 6, 6, 8, 8, 11, 10, 12, 9, 13, 13, 15, 11, 17, 16, 16, 15, 18, 16, 22, 22, 23, 22, 23, 20, 22, 22, 24, 22, 27, 22, 25, 25, 26, 24, 29, 24, 29, 30, 28, 27, 31, 31, 33, 32, 39, 35, 37, 34, 39, 36, 41, 38, 39, 37, 37, 34, 37, 39, 43, 38, 41, 40, 40, 39, 44, 40, 42, 42, 46, 47, 49, 46, 46, 47
Offset: 5

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A004347, A023837, A023838, A023839, A023840, A023841, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

  • Mathematica
    Table[PrimeOmega[Binomial[5 n, n - 5]], {n, 5, 81}] (* Ivan Neretin, Nov 08 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,n-5)); \\ Amiram Eldar, Jun 14 2025

Formula

From Amiram Eldar, Jun 14 2025: (Start)
a(n) = A001222(A004347(n)).
a(n) = A023841(n) - A001222(4*n+5) + A001222(n-4). (End)

Extensions

Offset corrected to 5 by Ivan Neretin, Nov 08 2017

A023843 Sum of exponents in prime-power factorization of C(5n,n+1).

Original entry on oeis.org

2, 5, 4, 7, 7, 10, 8, 11, 9, 12, 12, 15, 15, 15, 14, 17, 15, 18, 15, 21, 19, 20, 18, 22, 19, 24, 24, 25, 25, 27, 24, 26, 25, 24, 24, 28, 25, 29, 27, 32, 27, 33, 27, 30, 34, 33, 31, 33, 32, 35, 34, 40, 37, 40, 38, 41, 37, 42, 39, 46, 42, 42, 38, 40, 39, 42, 38, 42, 42, 43, 44, 47, 44, 46, 45, 48, 49
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A023837, A023839, A023840, A023841, A023842, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

  • Mathematica
    Table[PrimeOmega[Binomial[5 n, n + 1]], {n, 77}] (* Ivan Neretin, Nov 08 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,n+1)); \\ Amiram Eldar, Jun 14 2025

Formula

a(n) = A023837(n) + A001222(4*n) - A001222(n+1). - Amiram Eldar, Jun 14 2025

A023845 Sum of exponents in prime-power factorization of binomial(5n, n+3).

Original entry on oeis.org

1, 5, 4, 8, 7, 8, 9, 12, 9, 12, 13, 14, 14, 16, 13, 18, 15, 17, 16, 22, 17, 18, 20, 21, 19, 24, 23, 26, 24, 24, 24, 27, 23, 25, 25, 28, 24, 29, 28, 32, 29, 30, 28, 33, 31, 31, 31, 32, 32, 36, 33, 39, 36, 38, 38, 42, 35, 43, 42, 45, 41, 39, 38, 41, 40, 40, 38, 44, 41, 42, 45, 47, 43, 47, 44, 48, 48
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

  • Mathematica
    Table[Total[Transpose[FactorInteger[Binomial[5n,n+3]]][[2]]],{n,80}] (* Harvey P. Dale, Aug 12 2012 *)
a[n_] := PrimeOmega[Binomial[5*n, n+3]]; Array[a, 100] (* Amiram Eldar, Jun 14 2025 *)
  • PARI
    a(n) = bigomega(binomial(5*n,n+3)); \\ Amiram Eldar, Jun 14 2025

Formula

a(n) = A023844(n) + A001222(4*n-2) - A001222(n+3). - Amiram Eldar, Jun 14 2025

A023846 Sum of exponents in prime-power factorization of binomial(5n, n+4).

Original entry on oeis.org

0, 4, 5, 6, 6, 8, 10, 10, 10, 11, 12, 13, 15, 14, 14, 16, 15, 17, 16, 20, 19, 18, 18, 20, 19, 22, 25, 22, 23, 25, 24, 26, 24, 25, 24, 26, 25, 27, 30, 30, 28, 31, 29, 29, 31, 29, 31, 33, 32, 33, 33, 37, 36, 38, 39, 40, 38, 42, 40, 41, 40, 39, 39, 40, 39, 40, 39, 40, 43, 41, 43, 47, 43, 45, 47, 45, 46
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

By Kummer's theorem, a(n) is the sum over all primes p of the number of carries when n+4 is added to 4n-4 in base p. - Robert Israel, Nov 09 2017

Links

Crossrefs

Cf. A001222, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023847, A023848, A023849, A023850, A023851.

Programs

  • Maple
    seq(numtheory:-bigomega(binomial(5*n,n+4)), n=1..100); # Robert Israel, Nov 09 2017
  • Mathematica
    Table[PrimeOmega[Binomial[5 n, n + 4]], {n, 77}] (* Ivan Neretin, Nov 09 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n, n+4)); \\ Michel Marcus, Nov 09 2017

Formula

a(n) = A023844(n) + A001222(4*n-3) - A001222(n+4). - Amiram Eldar, Jun 14 2025

A023848 Sum of exponents in prime-power factorization of binomial(5n, 2n-1).

Original entry on oeis.org

1, 5, 4, 8, 6, 10, 11, 13, 11, 15, 13, 16, 16, 18, 18, 20, 18, 20, 18, 25, 21, 23, 22, 27, 24, 30, 28, 28, 28, 31, 32, 33, 29, 33, 32, 36, 32, 36, 37, 39, 35, 40, 32, 37, 38, 38, 39, 40, 40, 43, 41, 48, 44, 47, 47, 49, 45, 50, 47, 53, 50, 53, 50, 52, 50, 54, 50, 52, 53, 54, 57, 58, 55, 59, 57, 62
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023849, A023850, A023851.

Programs

  • Mathematica
    Table[PrimeOmega[Binomial[5 n, 2 n - 1]], {n, 77}] (* Ivan Neretin, Nov 09 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,2*n-1)); \\ Amiram Eldar, Jun 14 2025

Formula

a(n) = A023847(n) - A001222(3*n+1) + A001222(2*n). - Amiram Eldar, Jun 14 2025

A023849 Sum of exponents in prime-power factorization of binomial(5n, 2n-2).

Original entry on oeis.org

0, 3, 4, 7, 7, 8, 11, 13, 11, 11, 13, 15, 17, 18, 18, 18, 19, 18, 18, 25, 20, 21, 24, 26, 24, 27, 28, 28, 29, 29, 31, 33, 30, 30, 33, 34, 32, 36, 37, 38, 36, 34, 33, 37, 38, 36, 39, 40, 40, 42, 40, 47, 45, 45, 47, 48, 45, 47, 49, 52, 50, 52, 52, 51, 51, 50, 50, 54, 52, 52, 57, 58, 55, 56, 57, 60, 63
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023850, A023851.

Programs

  • Mathematica
    Table[PrimeOmega[Binomial[5 n, 2 n - 2]], {n, 77}] (* Ivan Neretin, Nov 09 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,2*n-2)); \\ Amiram Eldar, Jun 14 2025

Formula

a(n) = A023848(n) - A001222(3*n+2) + A001222(2*n-1). - Amiram Eldar, Jun 14 2025
Showing 1-10 of 13 results. Next

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

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