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A319567
Product of y divided by the GCD of y to the power of the length of y, where y is the integer partition with Heinz number n.
7
1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 4, 6, 1, 1, 4, 1, 3, 2, 5, 1, 2, 1, 6, 1, 4, 1, 6, 1, 1, 10, 7, 12, 4, 1, 8, 3, 3, 1, 8, 1, 5, 12, 9, 1, 2, 1, 9, 14, 6, 1, 8, 15, 4, 4, 10, 1, 6, 1, 11, 2, 1, 2, 10, 1, 7, 18, 12, 1, 4, 1, 12, 18, 8, 20, 12, 1, 3, 1, 13
OFFSET
0,6
COMMENTS
The Heinz number of a partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
FORMULA
a(n) = A003963(n) / A289508(n) ^ A001222(n).
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[n==1, 1, Times@@primeMS[n]/GCD@@primeMS[n]^PrimeOmega[n]], {n, 100}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 23 2018
STATUS
approved