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A328964
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Smallest k such that omega(k) * bigomega(k) = n, where omega = A001221, bigomega = A001222.
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9
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1, 2, 4, 8, 6, 32, 12, 128, 24, 30, 48, 2048, 60, 8192, 192, 120, 210, 131072, 240, 524288, 420, 480, 3072, 8388608, 840, 2310, 12288, 1920, 1680, 536870912, 3840, 2147483648, 3360, 7680, 196608, 9240, 6720, 137438953472, 786432, 30720, 13440, 2199023255552, 60060, 8796093022208
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OFFSET
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0,2
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their prime signatures begins:
1: ()
2: (1)
4: (2)
8: (3)
6: (1,1)
32: (5)
12: (2,1)
128: (7)
24: (3,1)
30: (1,1,1)
48: (4,1)
2048: (11)
60: (2,1,1)
8192: (13)
192: (6,1)
120: (3,1,1)
210: (1,1,1,1)
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MATHEMATICA
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dat=Table[PrimeOmega[n]*PrimeNu[n], {n, 1000}];
Table[Position[dat, i][[1, 1]], {i, First[Split[Union[dat], #2==#1+1&]]}]
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PROG
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(PARI) a(n)={if(n<1, 1, my(m=oo); fordiv(n, d, if(d<=n/d, m=min(m, 2^(n/d-d)*vecprod(primes(d))))); m)} \\ Andrew Howroyd, Nov 04 2019
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CROSSREFS
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Positions of first appearances in A113901.
Cf. A001221, A001222, A002110, A025487, A124010, A307409, A320632, A323023, A328956, A328958, A328959, A328962, A328963, A328965.
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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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