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A336856
Prime-shifted analog of gcd(d(n), sigma(n)): a(n) = gcd(A000005(n), A003973(n)).
6
1, 2, 2, 1, 2, 4, 2, 4, 1, 4, 2, 6, 2, 4, 4, 1, 2, 2, 2, 2, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 2, 4, 4, 4, 1, 2, 4, 4, 8, 2, 8, 2, 2, 2, 4, 2, 2, 1, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12, 2, 4, 6, 1, 4, 8, 2, 2, 4, 8, 2, 4, 2, 4, 6, 6, 4, 8, 2, 2, 1, 4, 2, 12, 4, 4, 4, 8, 2, 4, 4, 6, 4, 4, 4, 12, 2, 2, 2, 3, 2, 8, 2, 8, 8
OFFSET
1,2
FORMULA
a(n) = A009205(A003961(n)).
a(n) = gcd(A000005(n), A003973(n)) = gcd(A000005(n), A336841(n)).
a(n) = gcd(A000005(n), 2*A336840(n)).
a(n) = A003973(n) / A336838(n) = A000005(n) / A336839(n).
For n > 1, a(n) = A336841(n) / A336837(n).
For all primes p, and n >= 0, a(p^((2^n)-1)) = 2^n.
PROG
(PARI)
A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
A336856(n) = gcd(numdiv(n), A003973(n));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 12 2020
STATUS
approved