cp's OEIS Frontend

A380650 The largest number which is a linear combination of the divisors of n with nonnegative integer coefficients such that no linear combination with smaller nonnegative integer coefficients is equal to n.

%I A380650 #29 Feb 14 2025 14:25:10
%S A380650 0,1,2,3,4,7,6,7,8,13,10,17,12,19,22,15,16,25,18,31,32,31,22,37,24,37,
%T A380650 26,45,28,60,30,31,52,49,58,59,36,55,62,67,40,85,42,73,76,67,46,77,48,
%U A380650 73,82,87,52,79,94,97,92,85,58
%N A380650 The largest number which is a linear combination of the divisors of n with nonnegative integer coefficients such that no linear combination with smaller nonnegative integer coefficients is equal to n.
%C A380650 The mean of this sequence and Euler's totient function A000010 is approximately (but not exactly) equal to n.
%C A380650 The definition has evolved from a recreational question asked by P. M. Higgins, asking what maximal sum of money can be produced using British coins so no sum of one pound is produced by any subset of these coins.
%C A380650 The terms up to and including a(29)=28 agree with the formula a(n) = (A145388(n) - 1)/2, but a(30)=60, while the formula gives 67. This difference should be confirmed by an independent calculation using the definition in the name. - _Hugo Pfoertner_, Feb 14 2025
%e A380650 For n = 12, the largest sum is 17 = 0*1 + 0*2 + 1*3 + 2*4 + 1*6 = 0*1 + 0*2 + 3*3 + 2*4 + 0*6.
%e A380650 For n = 30, the largest sum is 60 = 1*1 + 0*2 + 0*3 + 0*5 + 4*6 + 2*10 + 1*15.
%Y A380650 Cf. A000010, A145388.
%K A380650 nonn
%O A380650 1,3
%A A380650 _Alexei Vernitski_, Jan 29 2025