A378665 Greatest non-abundant divisor of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 6, 13, 14, 15, 16, 17, 9, 19, 10, 21, 22, 23, 8, 25, 26, 27, 28, 29, 15, 31, 32, 33, 34, 35, 9, 37, 38, 39, 10, 41, 21, 43, 44, 45, 46, 47, 16, 49, 50, 51, 52, 53, 27, 55, 28, 57, 58, 59, 15, 61, 62, 63, 64, 65, 33, 67, 68, 69, 35, 71, 9, 73, 74, 75, 76, 77, 39, 79, 16, 81, 82, 83, 28

Offset

1,2

Comments

Largest term of A263837 that divides n.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = n / A378660(n).

a(n) >= A378664(n).

Example

For n=10, which is a non-abundant number because sigma(10) = 18 < 2*10, its greatest divisor that is not abundant is 10 itself, thus a(10) = 10.
For n=12, which is an abundant number because sigma(12) = 28 > 2*12, its greatest divisor that itself is not abundant is 6, as sigma(6) = 12. Thus a(12) = 6.

Mathematica

a[n_]:=Max[Select[Divisors[n], DivisorSigma[1, #]<=2# &]]; Array[a, 84] (* Stefano Spezia, Dec 06 2024 *)

Prog

(PARI)
A294935(n) = (sigma(n)<=(2*n));
A378665(n) = { fordiv(n, d, if(A294935(n/d), return(n/d))); (1); };

Crossrefs

Cf. A000203, A263837, A294935, A378660, A378664, A378735 [= a(A005101(n))].

Sequence in context: A334684 A062759 A327526 * A121758 A121759 A265310

Adjacent sequences: A378662 A378663 A378664 * A378666 A378667 A378668

Keyword

nonn

Author

Antti Karttunen, Dec 06 2024

Status

approved