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A339899
a(n) = gcd(A019565(2n)-1, A000265(phi(A019565(2n)))).
4
1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 5, 3, 1, 3, 1, 1, 1, 9, 1, 1, 1, 1, 1, 3, 1, 5, 1, 9, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 15, 1, 1, 1, 3, 5, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 1, 1, 3, 1, 3, 1, 1, 1, 27, 1, 1, 1, 1, 5, 3, 1, 1, 1, 81, 1, 1, 1, 3, 1, 1, 1, 9, 1, 3, 1
OFFSET
0,5
FORMULA
a(n) = gcd(A339809(2*n), A339971(n)), where A339971(n) = A053575(A019565(2n)).
a(n) = gcd(A339971(n), A339898(n)).
a(n) = A339971(n) / A339901(n).
a(n) = A000265(A049559(A019565(2*n))).
PROG
(PARI)
A000265(n) = (n>>valuation(n, 2));
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A339899(n) = { my(x=A019565(2*n)); gcd((x-1), A000265(eulerphi(x))); };
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 28 2020
STATUS
approved