A225882 -id:A225882 - cp's OEIS frontend

A225881 Numbers k that are equal to the product of the largest triangular proper divisor of k and the sum of all triangular proper divisors of k.

285, 5016, 24021, 142350, 145665, 154602, 204450, 318912, 474192, 843402, 1196690, 1283664, 1670250, 2739021, 3412950, 4255776, 5052135, 6054880, 6272140, 6433440, 6493728, 6650712, 6728190, 7156044, 7323030, 7797750, 9379350, 10108840, 10188864

Offset: 1

Antonio Roldán, May 19 2013

nonn

A triangular proper divisor of k is a positive triangular number less than k that divides k. - N. J. A. Sloane, Jul 04 2021

			5016 = 66*(66+6+3+1).

Donovan Johnson, Table of n, a(n) for n = 1..300

Cf. A000217, A225880, A225882.

pltQ[n_]:=Module[{d=Select[Divisors[n],OddQ[Sqrt[1+8#]]&]},n == Total[ d] Last[d]]; Select[Range[2,205000],pltQ] (* The program generates the first 7 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Jul 03 2021 *)

msumprop(n)={k=1;i=1;s=0;d=1;while(k<=n\2,if(n/k==n\k,d=k;s+=d);i+=1;k+=i);s*=d;return(s)}
{for (n=2,10^7,if(n==msumprop(n),print(n)))}

A225880 Numbers that can be expressed as the product of largest odd proper divisor and the sum of odd proper divisors.

Original entry on oeis.org

12, 56, 672, 992, 11904, 16256, 55552, 195072, 666624, 910336, 10924032, 16125952, 67100672, 193511424, 805208064, 903053312, 3757637632, 10836639744, 17179738112, 45091651584, 66563866624, 206156857344, 274877382656, 798766399488, 962065334272, 1090788524032

Offset: 1

Antonio Roldán, May 19 2013

nonn

The numbers a(n) can be expressed as 2^(m+n+p+...)*(2^m-1)*(2^n-1)*(2^p-1)... with 2^m-1, 2^n-1, 2^p-1 distinct Mersenne primes (A000668(n)). Example: 55552 = 2^6*7*31=2^6*(2^3-1)*(2^5-1).
This sequence is supersequence of A139256.
The number a(n) is in A139256 or a(n) is product of twice even perfect numbers A139256(n). Example: 1090788524032 = 16256*67100672 = (2*8128)*(2*33550336) = A139256(4) * A139256(5).

			11904 = 93*(93+31+3+1).

Cf. A225882, A225881.

gdivodd(n)={m=n;while(m/2==m\2,m=m/2);return(m)}
{for (n=2,2*10^8,m=gdivodd(n)*sumdiv(n, d, d*(d%2));if(m==n,print(n)))}

cp's OEIS Frontend

A225881 Numbers k that are equal to the product of the largest triangular proper divisor of k and the sum of all triangular proper divisors of k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI