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A322361
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a(n) = gcd(n, A003961(n)), where A003961 is completely multiplicative with a(prime(k)) = prime(k+1).
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19
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1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 7, 9, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 1, 9, 1, 1, 5, 1, 11, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 35
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OFFSET
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1,6
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := If[n == 1, 1, GCD[n, Times@@(NextPrime[First[#]]^Last[#] &/@FactorInteger[n])]]; Array[a, 100] (* Amiram Eldar, Dec 05 2018~ *)
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PROG
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(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
(Python)
from math import gcd, prod
from sympy import nextprime, factorint
def A322361(n): return gcd(n, prod(nextprime(p)**e for p, e in factorint(n).items())) # Chai Wah Wu, Dec 26 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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STATUS
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approved
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