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A326844
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Let y be the integer partition with Heinz number n. Then a(n) is the size of the complement, in the minimal rectangular partition containing the Young diagram of y, of the Young diagram of y.
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22
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0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 3, 1, 0, 0, 1, 0, 4, 2, 4, 0, 3, 0, 5, 0, 6, 0, 3, 0, 0, 3, 6, 1, 2, 0, 7, 4, 6, 0, 5, 0, 8, 2, 8, 0, 4, 0, 2, 5, 10, 0, 1, 2, 9, 6, 9, 0, 5, 0, 10, 4, 0, 3, 7, 0, 12, 7, 4, 0, 3, 0, 11, 1, 14, 1, 9, 0, 8, 0, 12, 0, 8, 4, 13, 8, 12, 0, 4, 2, 16, 9, 14, 5, 5, 0, 3, 6, 4
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OFFSET
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1,10
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COMMENTS
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The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
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LINKS
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FORMULA
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EXAMPLE
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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 . . .
The size of the complement (shown in dots) in a 6 X 4 rectangle is 5, so a(7865) = 5.
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MATHEMATICA
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Table[If[n==1, 0, With[{y=Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]}, Max[y]*Length[y]-Total[y]]], {n, 100}]
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PROG
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(PARI)
A056239(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1])));
A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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