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A353274
a(n) = gcd(n, A353272(n)).
5
1, 2, 3, 1, 5, 2, 7, 1, 1, 2, 11, 1, 13, 2, 3, 1, 17, 2, 19, 5, 3, 2, 23, 1, 1, 2, 1, 7, 29, 2, 31, 1, 3, 2, 5, 1, 37, 2, 3, 5, 41, 6, 43, 11, 1, 2, 47, 3, 1, 2, 3, 13, 53, 2, 5, 7, 3, 2, 59, 1, 61, 2, 7, 1, 5, 2, 67, 17, 3, 2, 71, 1, 73, 2, 3, 19, 7, 2, 79, 5, 1, 2, 83, 1, 5, 2, 3, 11, 89, 2, 7, 23, 3, 2, 5, 3, 97
OFFSET
1,2
FORMULA
a(n) = gcd(n, A353272(n)) = gcd(n, A353273(n)) = gcd(A353272(n), A353273(n)).
a(p) = p for all primes p.
PROG
(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A332449(n) = A005940(1+(3*A156552(n)));
A353274(n) = { my(u=A332449(n)); gcd(n, (u / gcd(n, u))); };
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 09 2022
STATUS
approved