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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.
3
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
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
KEYWORD
nonn
AUTHOR
Antonio Roldán, May 19 2013
STATUS
approved