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A175849
Numbers k with property that sum of divisors of k-th triangular number is some m-th triangular number.
3
1, 8, 9, 215, 458, 520, 2232, 3251, 3634, 5349, 9489, 10051, 10463, 14072, 14705, 17463, 27812, 46552, 55889, 79614, 100055, 106941, 110682, 113839, 119098, 181690, 197223, 214600, 270570, 287585, 333291, 384463, 439206, 443115, 608563, 767496, 1097448, 1335300
OFFSET
1,2
LINKS
FORMULA
sigma(T(k)) = T(m); A000203(A000217(k)) = A000217(m).
EXAMPLE
Some pairs of k,m: 1,1; 8,13; 9,12; 215,384; 458,575; 520,783; 2232,4095; 3251,4607; 3634,4095; 5349,6912; 9489,12543; 10051,13824.
MATHEMATICA
Select[Range[10^4], IntegerQ @ Sqrt[8*DivisorSigma[1, #*(#+1)/2] + 1] &] (* Amiram Eldar, Feb 23 2020 *)
PROG
(PARI) {for(n=1, 10^7, m=sigma(n*(n+1)/2); issquare(d=1+8*m) && print1(n, ", "))} \\ edited by
CROSSREFS
Cf. A000203 (sigma(n) = sum of divisors of n), A000217 (triangular numbers), A175850 (corresponding values of m).
Sequence in context: A041141 A041142 A307947 * A294468 A041605 A239524
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 27 2010
EXTENSIONS
More terms from Amiram Eldar, Feb 23 2020
STATUS
approved