The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.
(history; published version)

#9 by Susanna Cuyler at Fri Jan 17 17:42:05 EST 2020

STATUS

proposed

approved

#8 by Gus Wiseman at Fri Jan 17 13:55:56 EST 2020

STATUS

editing

proposed

#7 by Gus Wiseman at Fri Jan 17 13:55:28 EST 2020

CROSSREFS

Row lengths of A331385.

#6 by Gus Wiseman at Fri Jan 17 13:54:53 EST 2020

CROSSREFS

Converges to A014692.

#5 by Gus Wiseman at Fri Jan 17 13:54:33 EST 2020

CROSSREFS

The n-th prime number minus n plus one is A014692(n).

Converges to A014692.

#4 by Gus Wiseman at Fri Jan 17 13:53:13 EST 2020

CROSSREFS

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

#3 by Gus Wiseman at Fri Jan 17 12:00:55 EST 2020

CROSSREFS

Partitions whose product divides their sum of primes are A331381.

Partitions whose product equals their sum of primes are A331383.

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

#2 by Gus Wiseman at Fri Jan 17 11:59:24 EST 2020

NAME

allocated for Gus WisemanIf A331417(n) is the maximum sum of primes of the parts of an integer partition of n, then a(n) = A331417(n) - n + 1.

DATA

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

Row lengths of A331385.

Sum of prime factors is A001414.

Partitions into primes are A000607.

The n-th prime number minus n plus one is A014692(n).

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

Partitions whose product divides their sum of primes are A331381.

Partitions whose product equals their sum of primes are A331383.

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

KEYWORD

allocated

nonn

AUTHOR

Gus Wiseman, Jan 17 2020

STATUS

approved

editing

#1 by Gus Wiseman at Thu Jan 16 18:17:36 EST 2020

NAME

allocated for Gus Wiseman

KEYWORD

allocated

STATUS

approved