A355003 a(n) = gcd(A003415(n), A277791(n)), where A003415 is the arithmetic derivative and A277791 is the denominator of sum of reciprocals of proper divisors of n.

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 4, 1, 1, 1, 8, 1, 3, 1, 4, 1, 1, 1, 4, 5, 1, 9, 4, 1, 1, 1, 16, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 4, 3, 1, 1, 16, 7, 5, 1, 4, 1, 27, 1, 4, 1, 1, 1, 4, 1, 1, 3, 32, 1, 1, 1, 4, 1, 1, 1, 12, 1, 1, 5, 4, 1, 1, 1, 16, 27, 1, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 1, 1, 16, 1, 7, 3, 5, 1, 1, 1, 4, 1

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = gcd(A003415(n), A277791(n)).

a(p^k) = p^(k-1) for all primes p and exponents k > 0.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A277791(n) = denominator((sigma(n)-1)/n); \\ From A277791
A355003(n) = gcd(A003415(n), A277791(n));

Crossrefs

Cf. A003415, A277791.

Cf. also A355815.

Sequence in context: A128708 A087653 A295666 * A322020 A294895 A285328

Adjacent sequences: A355000 A355001 A355002 * A355004 A355005 A355006

Keyword

nonn

Author

Antti Karttunen, Jul 18 2022

Status

approved