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A333129
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Product of all distinct least part primes from all partitions of n into prime parts.
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6
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1, 1, 2, 3, 2, 10, 6, 14, 6, 6, 30, 66, 30, 78, 42, 30, 30, 510, 210, 570, 210, 210, 330, 690, 2310, 210, 2730, 210, 2310, 6090, 30030, 6510, 2730, 2310, 39270, 2310, 46410, 85470, 3990, 30030, 39270, 94710, 570570, 1291290, 30030, 30030, 903210, 1411410, 746130
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OFFSET
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0,3
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COMMENTS
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For all n, omega(a(n)) = Omega(a(n)). The prime factorization of each term gives the least part primes of all partitions of n into prime parts.
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LINKS
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EXAMPLE
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a(2) = 2 because [2] is the only prime partition of 2. a(5) = 10 because the prime partitions of 5 are [2,3] and [5], so the products of all distinct least part primes is 2*5 = 10.
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MAPLE
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b:= proc(n, p, t) option remember; `if`(n=0, 1, `if`(p>n, 0, (q->
add(b(n-p*j, q, 1), j=1..n/p)*t^p+b(n, q, t))(nextprime(p))))
end:
a:= n-> (p-> mul(`if`(coeff(p, x, i)>0, i, 1), i=2..n))(b(n, 2, x)):
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MATHEMATICA
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a[0] = 1; a[n_] := Times @@ Union[Min /@ IntegerPartitions[n, All, Prime[ Range[PrimePi[n]]]]];
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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