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A350756
Integers whose number of divisors that are triangular numbers sets a new record.
4
1, 3, 6, 30, 90, 180, 210, 420, 630, 1260, 2520, 6930, 13860, 27720, 41580, 83160, 138600, 180180, 360360, 540540, 1081080, 1413720, 2162160, 3063060, 6126120, 12252240, 18378360, 36756720, 73513440, 91891800, 116396280, 183783600, 232792560, 349188840
OFFSET
1,2
COMMENTS
Terms that are triangular: 1, 3, 6, 210, 630, 2162160, ...
The number of triangular divisors of a(n) is A007862(a(n)): 1, 2, 3, 5, 6, 7, 8, 9, 10, 12, ...
EXAMPLE
1260 has 36 divisors of which 12 are triangular numbers {1, 3, 6, 10, 15, 21, 28, 36, 45, 105, 210, 630}. No positive integer smaller than 1260 has as many as twelve triangular divisors; hence 1260 is a term.
MATHEMATICA
max=0; Do[If[(d=Length@Select[Divisors@k, IntegerQ[(Sqrt[8#+1]-1)/2]&])>max, Print@k; max=d], {k, 10^10}] (* Giorgos Kalogeropoulos, Jan 13 2022 *)
PROG
(PARI) lista(nn) = my(r=0); for (n=1, nn, my(m = sumdiv(n, d, ispolygonal(d, 3))); if (m>r, r=m; print1(n, ", ")); ); } \\ Michel Marcus, Jan 14 2022
CROSSREFS
Similar for A046952 (squares), A053624 (odd), A093036 (palindromes), A181808 (even), A340548 (repdigits), A340549 (repunits) divisors.
Sequence in context: A211168 A355989 A215294 * A090932 A361864 A280981
KEYWORD
nonn
AUTHOR
Bernard Schott, Jan 13 2022
STATUS
approved