A375228 - OEIS

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 #7 Aug 06 2024 11:13:27

%S 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 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 1,1,59,1,61,8,31,64,32,1,67,2,52,1,71,1,73,4,37

%N 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 Amiram Eldar, <a href="/A375228/b375228.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 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 (PARI) usigma(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]);}

%o a(n) = {my(k = n); while((n % usigma(k)), k--); k;}

%Y The unitary analog of A319068.

%Y Cf. A034448.

%K nonn

%O 1,3

%A _Amiram Eldar_, Aug 06 2024