OFFSET
1,15
COMMENTS
The internal portion of an integer partition consists of all squares in the Young diagram that have a square both directly below and directly to the right.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
EXAMPLE
The partition with Heinz number 7865 is (6,5,5,3), with diagram
o o o o o o
o o o o o
o o o o o
o o o
with internal portion
o o o o o
o o o o
o o o
of size 12, so a(7865) = 12.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[n==1, 0, Total[primeMS[n]]-Max[primeMS[n]]-Length[primeMS[n]]+Length[Union[primeMS[n]]]], {n, 100}]
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 05 2019
EXTENSIONS
More terms from Antti Karttunen, Apr 14 2019
STATUS
approved