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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.
7
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).
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.
Sequence in context: A166159 A169693 A180121 * A062890 A259626 A058586
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 17 2020
STATUS
approved