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.

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, 26, 45, 28, 60, 30, 31, 52, 49, 58, 59, 36, 55, 62, 67, 40, 85, 42, 73, 76, 67, 46, 77, 48, 73, 82, 87, 52, 79, 94, 97, 92, 85, 58

Offset

1,3

Comments

The mean of this sequence and Euler's totient function A000010 is approximately (but not exactly) equal to n.

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.

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

Links

Table of n, a(n) for n=1..59.

Example

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.
For n = 30, the largest sum is 60 = 1*1 + 0*2 + 0*3 + 0*5 + 4*6 + 2*10 + 1*15.

Crossrefs

Cf. A000010, A145388.

Sequence in context: A265363 A319651 A373185 * A340632 A074846 A120225

Adjacent sequences: A380647 A380648 A380649 * A380651 A380652 A380653

Keyword

nonn

Author

Alexei Vernitski, Jan 29 2025

Status

approved