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

1,3

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A143539 A249063 A362687 * A099307 A361869 A256750

Adjacent sequences: A341876 A341877 A341878 * A341880 A341881 A341882

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 22 2021

Status

approved