A331418 If A331417(n) is the maximum sum of primes of the parts of an integer partition of n, then a(n) = A331417(n) - n + 1.

1, 2, 3, 4, 5, 7, 8, 11, 12, 15, 20, 21, 26, 29, 30, 33, 38, 43, 44, 49, 52, 53, 58, 61, 66, 73, 76, 77, 80, 81, 84, 97, 100, 105, 106, 115, 116, 121, 126, 129, 134, 139, 140, 149, 150, 153, 154, 165, 176, 179, 180, 183, 188, 189, 198, 203, 208, 213, 214, 219

Offset

0,2

Comments

For n > 4, a(n) = A014692(n).

Links

Table of n, a(n) for n=0..59.

Formula

a(n) = A331417(n) - n + 1.

Mathematica

Table[Max@@Table[Total[Prime/@y], {y, IntegerPartitions[n]}]-n+1, {n, 0, 30}]

Crossrefs

Converges to A014692.

Row lengths of A331385.

Sum of prime factors is A001414.

Partitions into primes are A000607.

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

Cf. A000040, A014689, A056239, A330950, A330953, A330954, A331378, A331381, A331383, A331387, A331415, A331416.

Sequence in context: A166159 A169693 A180121 * A062890 A259626 A058586

Adjacent sequences: A331415 A331416 A331417 * A331419 A331420 A331421

Keyword

nonn

Author

Gus Wiseman, Jan 17 2020

Status

approved