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A326837
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Heinz numbers of integer partitions whose length and maximum both divide their sum.
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30
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2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 84, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197
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OFFSET
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1,1
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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).
The enumeration of these partitions by sum is given by A326843.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
2: {1}
3: {2}
4: {1,1}
5: {3}
7: {4}
8: {1,1,1}
9: {2,2}
11: {5}
13: {6}
16: {1,1,1,1}
17: {7}
19: {8}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
30: {1,2,3}
31: {11}
32: {1,1,1,1,1}
37: {12}
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MAPLE
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isA326837 := proc(n)
psigle := numtheory[bigomega](n) ;
if modp(psigsu, psigma) = 0 and modp(psigsu, psigle) = 0 then
true;
else
false;
end if;
end proc:
n := 1:
for i from 2 to 3000 do
if isA326837(i) then
printf("%d %d\n", n, i);
n := n+1 ;
end if;
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MATHEMATICA
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Select[Range[2, 100], With[{y=Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]}, Divisible[Total[y], Max[y]]&&Divisible[Total[y], Length[y]]]&]
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CROSSREFS
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Cf. A001222, A047993, A056239, A061395, A067538, A112798, A316413, A326836, A326843, A326847, A326848.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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