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A342455
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The fifth powers of primorials: a(n) = A002110(n)^5.
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2
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1, 32, 7776, 24300000, 408410100000, 65774855015100000, 24421743243121524300000, 34675383095948798128025100000, 85859681408495723096004822084900000, 552622359415801587878908964592391520700000, 11334919554709059323420895730190266747414284300000, 324509123504618420438174660414872405442002404781629300000
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OFFSET
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0,2
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COMMENTS
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The ratio G(n) = sigma(n) / (exp(gamma)*n*log(log(n))), where gamma is the Euler-Mascheroni constant (A001620), as applied to these numbers from a(1)=32 onward, develops as:
1: 0.8893323133
2: 0.7551575418
3: 0.7303870617
4: 0.7347890824
5: 0.7263701246
6: 0.7298051649
7: 0.7304358358
8: 0.7354921494
9: 0.7389343933
10: 0.7391912616
11: 0.7416291350
12: 0.7424159544
...
Notably, after its minimum at term a(5) = 65774855015100000, it starts increasing again, albeit rather slowly. At n=10000 the ratio is 0.8632750..., and at n=40000, it is 0.87545260... Question: Does this trend continue indefinitely? In contrast, for primorials, A002110, the ratio appears to be monotonically decreasing, see comments in A342000.
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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(PARI) A342455(n) = prod(i=1, n, prime(i))^5;
(Python)
from sympy.ntheory.generate import primorial
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CROSSREFS
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Diagonal in A079474. After the initial term, also the leftmost branch in that subtree of A329886 whose root is 32.
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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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