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A316436
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Sum divided by GCD of the integer partition with Heinz number n > 1.
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1
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1, 1, 2, 1, 3, 1, 3, 2, 4, 1, 4, 1, 5, 5, 4, 1, 5, 1, 5, 3, 6, 1, 5, 2, 7, 3, 6, 1, 6, 1, 5, 7, 8, 7, 6, 1, 9, 4, 6, 1, 7, 1, 7, 7, 10, 1, 6, 2, 7, 9, 8, 1, 7, 8, 7, 5, 11, 1, 7, 1, 12, 4, 6, 3, 8, 1, 9, 11, 8, 1, 7, 1, 13, 8, 10, 9, 9, 1, 7, 4, 14, 1, 8, 10, 15, 6, 8, 1, 8, 5, 11, 13, 16, 11, 7, 1, 9, 9, 8, 1, 10, 1, 9, 9
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OFFSET
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2,3
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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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MAPLE
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a:= n-> (l-> add(i, i=l)/igcd(l[]))(map(i->
numtheory[pi](i[1])$i[2], ifactors(n)[2])):
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MATHEMATICA
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Table[With[{pms=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]}, Total[pms]/GCD@@pms], {n, 2, 100}]
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PROG
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(PARI) A316436(n) = { my(f = factor(n), pis = apply(p -> primepi(p), f[, 1]~), es = f[, 2]~, g = gcd(pis)); sum(i=1, #f~, pis[i]*es[i])/g; }; \\ Antti Karttunen, Sep 10 2018
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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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