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

1,1

Comments

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

Links

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

Example

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

Mathematica

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 *)

Prog

(PARI)
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)))}

Crossrefs

Cf. A000217, A225880, A225882.

Sequence in context: A105921 A209311 A176712 * A332919 A278629 A241970

Adjacent sequences: A225878 A225879 A225880 * A225882 A225883 A225884

Keyword

nonn

Author

Antonio Roldán, May 19 2013

Status

approved