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 1-2 of 2 results.

A109490 Value of Product[k/sd(k,3),k=1..n], where sd[k,b] is the sum of the digits of k represented in base b.

Original entry on oeis.org

1, 1, 3, 6, 10, 30, 70, 140, 1260, 6300, 23100, 138600, 600600, 2102100, 10510500, 42042000, 142942800, 1286485200, 8147739600, 40738698000, 285170886000, 1568439873000, 7214823415800, 43288940494800, 216444702474000
Offset: 1

Views

Author

John W. Layman, Jun 29 2005

Keywords

Comments

See A109489 for the corresponding base-2 sequence.
For n=601 the sum is not an integer (its denominator is 7). B-file contains all terms before that.

Crossrefs

Cf. A109489.

Programs

  • Maple
    P:= 1: A[1]:= P:
    for n from 2 to 100 do
      P:= P*n/convert(convert(n,base,3),`+`);
      A[n]:= P;
    od:
    seq(A[i],i=1..100); # Robert Israel, Jan 21 2018

A109491 Value of Product_{k=1..n} sigma(k)/sd(k,2), where sd(k,b) is the sum of the digits of k represented in base b.

Original entry on oeis.org

1, 3, 6, 42, 126, 756, 2016, 30240, 196560, 1769040, 7076160, 99066240, 462309120, 3698472960, 22190837760, 687915970560, 6191243735040, 120729252833280, 804861685555200, 16902095396659200, 180289017564364800
Offset: 1

Views

Author

John W. Layman, Jun 29 2005

Keywords

Comments

Surprisingly, the product in the definition is an integer for all values of n for which it has been calculated (1-300), whereas the corresponding base-3 product is not.
The product is an integer at least for n <= 80000. - Robert Israel, Jan 22 2018

Examples

			The divisors of 1-5 are {1}, {1,2}, {1,3}, {1,2,4} and {1,5}, respectively and the base-2 representations of 1-5 are 1,10,11,100,101, so a(5)=(1/1)(3/1)(4/2)(7/1)(6/2)=126.
		

Crossrefs

Cf. A109489.

Programs

  • Maple
    p:= 1: A[1]:= 1:
    for n from 2 to 50 do
    p:= p * numtheory:-sigma(n)/convert(convert(n,base,2),`+`);
    A[n]:= p;
    od:
    seq(A[i],i=1..50); # Robert Israel, Jan 22 2018
  • PARI
    a(n) = prod(k=1, n, sigma(k)/hammingweight(k)); \\ Michel Marcus, Jul 10 2014

Extensions

Offset corrected to 1 by Michel Marcus, Jul 10 2014
Showing 1-2 of 2 results.