A078934 -id:A078934

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Search: a078934 -id:a078934

Displaying 1-2 of 2 results found.

page 1

A078935

Largest divisor of n*(n+1)/2 that is <= sqrt(n*(n+1)/2).

+10
2

1, 1, 2, 2, 3, 3, 4, 6, 5, 5, 6, 6, 7, 7, 10, 8, 9, 9, 10, 14, 11, 11, 12, 15, 13, 13, 18, 14, 15, 15, 16, 22, 17, 17, 21, 18, 19, 19, 26, 20, 21, 21, 22, 30, 23, 23, 24, 28, 35, 25, 34, 26, 27, 33, 35, 38, 29, 29, 30, 30, 31, 31, 42, 40, 39, 33, 34, 46, 35, 35, 36, 36, 37, 37, 50

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Smaller side of integral rectangle with area n*(n+1)/2 having minimal semiperimeter;

a(n) = A033676(A000217(n));

a(n) = A078934(n) - A078936(n); a(n)*A078936(n) = A000217(n).

LINKS

Table of n, a(n) for n=1..75.

MATHEMATICA

ld[n_]:=Last[Select[Divisors[n], #<=Sqrt[n]&]]; ld/@Accumulate[ Range[ 80]] (* Harvey P. Dale, Jun 19 2021 *)

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 17 2002

STATUS

approved

A078936

Smallest divisor of n*(n+1)/2 that is >= sqrt(n*(n+1)/2).

+10
2

1, 3, 3, 5, 5, 7, 7, 6, 9, 11, 11, 13, 13, 15, 12, 17, 17, 19, 19, 15, 21, 23, 23, 20, 25, 27, 21, 29, 29, 31, 31, 24, 33, 35, 30, 37, 37, 39, 30, 41, 41, 43, 43, 33, 45, 47, 47, 42, 35, 51, 39, 53, 53, 45, 44, 42, 57, 59, 59, 61, 61, 63, 48, 52, 55, 67, 67, 51, 69, 71, 71, 73

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Greater side of integral rectangle with area n*(n+1)/2 having minimal semiperimeter.

LINKS

Table of n, a(n) for n=1..72.

FORMULA

a(n) = A033677(A000217(n)).

a(n) = A078934(n) - A078935(n)

a(n)*A078935(n) = A000217(n).

MATHEMATICA

a[n_] := Select[Divisors[n*(n+1)/2], # >= Sqrt[n*(n+1)/2] &, 1][[1]]; Array[a, 100] (* Amiram Eldar, Aug 03 2024 *)

CROSSREFS

Cf. A000217, A033677, A078934, A078935.