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

Author

Gus Wiseman, Jan 17 2020

Keywords

• nonn

Comments

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

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.

Programs

Mathematica

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

Formula

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