A331417 Maximum sum of primes of the parts of an integer partition of n.

0, 2, 4, 6, 8, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset: 0

Author

Gus Wiseman, Jan 17 2020

Keywords

• nonn

Comments

For n > 4, a(n) = prime(n).

Crossrefs

Converges to A000040.

Row lengths of A331416.

The corresponding minimum is A007494.

Partitions whose sum of primes is divisible by their sum are A331379.

Cf. A000607, A001414, A014689, A056239, A179437, A330950, A330953, A330954, A331381, A331383, A331385, A331387, A331415, A331418.

Programs

Mathematica

Table[Max@@Table[Total[Prime/@y],{y,IntegerPartitions[n]}],{n,0,10}]

Formula

a(n) = A331418(n) + n - 1.