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

Author

Antti Karttunen, Dec 06 2024

Keywords

• nonn

Comments

Largest term of A263837 that divides n.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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

a(n) >= A378664(n).