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).

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

Offset: 1

Author

Amiram Eldar, Aug 06 2024

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Bhabesh Das and Helen K. Saikia, On the Sum of Unitary Divisors Maximum Function, AIMS Mathematics, Vol. 2, No. 1 (2017), pp. 96-101.

Crossrefs

The unitary analog of A319068.

Cf. A034448.

Programs

Mathematica

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]

PARI

usigma(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]);}
a(n) = {my(k = n); while((n % usigma(k)), k--); k;}