A225880 -id:A225880 - 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)))}

A225882 Numbers k such that core(k) is equal to the sum of the proper square divisors of k, where core(k) = A007913(k).

Original entry on oeis.org

20, 90, 336, 650, 5440, 7371, 13000, 14762, 28730, 30240, 83810, 87296, 130682, 147420, 218400, 280370, 295240, 406875, 708122, 924482, 1397760, 1875530, 2613640, 3536000, 4881890, 4960032, 5884851, 7856640, 7893290, 8137500

Offset: 1

Antonio Roldán, May 19 2013

nonn

If p is prime and p^2 + 1 squarefree, then p^2*(p^2 + 1) is in the sequence.

			13000 is a term because core(13000) = 130 = 100 + 25 + 4 + 1.

Giovanni Resta, Table of n, a(n) for n = 1..282 (terms < 5*10^11; first 80 terms from Charles R Greathouse IV)

Cf. A007913, A035316, A225880, A225881.

for(n=2,10^8,if(core(n)==sumdiv(n,d,d*issquare(d)),print(n)))

ssd(f)=prod(i=1,#f[,1],(f[i,1]^(f[i,2]+2-f[i,2]%2)-1)/(f[i,1]^2-1))
is(n)=my(f=factor(n));prod(i=1,#f[,1],f[i,1]^(f[i,2]%2))==ssd(f) && n>1 \\ Charles R Greathouse IV, May 20 2013

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.

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A225882 Numbers k such that core(k) is equal to the sum of the proper square divisors of k, where core(k) = A007913(k).

Views

Author

Keywords

Comments

Examples

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Crossrefs

Programs

PARI

PARI