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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.

%I A341879 #30 Apr 28 2021 02:05:13
%S A341879 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,
%T A341879 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,
%U A341879 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
%N 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.
%H A341879 Seiichi Manyama, <a href="/A341879/b341879.txt">Table of n, a(n) for n = 1..10000</a>
%e A341879 k that satisfies sigma(k) = 12 is 6 or 11. d(6) = 4 and d(11) = 2. So a(12) = 4.
%t A341879 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 *)
%o A341879 (PARI) a(n) = my(m=0); for(k=1, n, if(sigma(k)==n, m=max(m, numdiv(k)))); m;
%Y A341879 Cf. A000005, A000203, A054973, A057637, A085790, A299762.
%K A341879 nonn,easy
%O A341879 1,3
%A A341879 _Seiichi Manyama_, Feb 22 2021