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A375228 a(n) is the largest number k such that usigma(k) divides n where usigma(k) is the sum of unitary divisors of k (A034448).

%I A375228 #7 Aug 06 2024 11:13:27
%S A375228 1,1,2,3,4,5,1,7,8,9,1,11,1,13,4,7,16,17,1,19,2,1,1,23,4,25,8,27,1,29,
%T A375228 1,31,32,16,4,24,1,37,2,28,1,41,1,43,8,1,1,47,1,49,16,25,1,53,4,39,2,
%U A375228 1,1,59,1,61,8,31,64,32,1,67,2,52,1,71,1,73,4,37
%N A375228 a(n) is the largest number k such that usigma(k) divides n where usigma(k) is the sum of unitary divisors of k (A034448).
%H A375228 Amiram Eldar, <a href="/A375228/b375228.txt">Table of n, a(n) for n = 1..10000</a>
%H A375228 Bhabesh Das and Helen K. Saikia, <a href="http://dx.doi.org/10.3934/Math.2017.1.96">On the Sum of Unitary Divisors Maximum Function</a>, AIMS Mathematics, Vol. 2, No. 1 (2017), pp. 96-101.
%t A375228 usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); usigma[1] = 1; a[n_] := Module[{k = n}, While[!Divisible[n, usigma[k]], k--]; k]; Array[a, 100]
%o A375228 (PARI) usigma(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]);}
%o A375228 a(n) = {my(k = n); while((n % usigma(k)), k--); k;}
%Y A375228 The unitary analog of A319068.
%Y A375228 Cf. A034448.
%K A375228 nonn
%O A375228 1,3
%A A375228 _Amiram Eldar_, Aug 06 2024