A341879 a(n) is the largest d(k) such that sigma(k) = n, where d is the number of divisor function and sigma is the sum of divisors function.

1, 0, 2, 2, 0, 2, 3, 2, 0, 0, 0, 4, 3, 2, 4, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 0, 0, 6, 0, 2, 5, 4, 0, 0, 0, 4, 0, 2, 6, 4, 0, 6, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 6, 3, 0, 0, 8, 0, 2, 6, 0, 0, 0, 0, 2, 0, 0, 0, 8, 0, 2, 0, 0, 0, 6, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 8, 9, 0, 6, 0, 0, 8, 0, 6, 0, 0, 0, 2, 0, 6, 0

Offset: 1

Author

Seiichi Manyama, Feb 22 2021

Keywords

• nonn
• easy

Examples

			k that satisfies sigma(k) = 12 is 6 or 11. d(6) = 4 and d(11) = 2. So a(12) = 4.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000203, A054973, A057637, A085790, A299762.

Programs

Mathematica

a[n_] := Module[{dmax = 0}, Do[If[DivisorSigma[1, k] == n && (d = DivisorSigma[0, k]) > dmax, dmax = d], {k, 1, n}]; dmax]; Array[a, 100] (* Amiram Eldar, Apr 28 2021 *)

PARI

a(n) = my(m=0); for(k=1, n, if(sigma(k)==n, m=max(m, numdiv(k)))); m;