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

0,2

Comments

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

Links

Table of n, a(n) for n=0..57.

Formula

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

Mathematica

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

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.

Sequence in context: A027919 A174058 A186382 * A077473 A200738 A129896

Adjacent sequences: A331414 A331415 A331416 * A331418 A331419 A331420

Keyword

nonn

Author

Gus Wiseman, Jan 17 2020

Status

approved