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A354411
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a(n) is the least oblong number that is divisible by the first n primes.
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0
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2, 6, 30, 210, 43890, 510510, 510510, 3967173210, 134748093480, 530514844860, 4201942828713630, 1706257740074998110, 125050509312845636520, 511284700554162118403820, 2695009287439086535873235280, 206794067314254446263154097180, 86753583273488685998907289046220
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) <= (m-1)*m, where m = A002110(n).
(End)
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EXAMPLE
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2, 3, and 5 are the first three primes. The first oblong number that is a multiple of all three first primes is 30. So, a(3) = 30.
The first oblong number that is a multiple of primorial(5) = 2310 is 19*2310 = 43890, so a(5) = 43890.
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PROG
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(Python)
from sympy import integer_nthroot, primorial
def oblong(n): r = integer_nthroot(n, 2)[0]; return r*(r+1) == n
def a(n):
m = psharp = primorial(n)
while not oblong(m): m += psharp
return m
from sympy import primorial
def a(n): return (m := A344005(primorial(n)))*(m+1)
a344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m)))
a(n) = my(m=a344005(a002110(n))); m*(m+1) \\ Felix Fröhlich, May 31 2022
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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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