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A342671
a(n) = gcd(sigma(n), A003961(n)), where A003961 is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors of n.
41
1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 21, 1, 3, 1, 15, 1, 3, 5, 1, 1, 3, 1, 9, 1, 3, 1, 1, 1, 3, 1, 9, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 15, 1, 3, 5, 3, 1, 21, 1, 3, 1, 1, 7, 3, 1, 9, 1, 3, 1, 15, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 5, 9, 1, 3, 1, 3, 1, 3, 1, 9, 1, 3, 13, 7, 1, 3, 1, 3, 1
OFFSET
1,2
FORMULA
a(n) = gcd(A000203(n), A003961(n)).
a(n) = gcd(A000203(n), A286385(n)) = gcd(A003961(n), A286385(n)).
a(n) = A341529(n) / A342672(n).
From Antti Karttunen, Jul 21 2022: (Start)
a(n) = A003961(n) / A349161(n).
a(n) = A000203(n) / A349162(n).
a(n) = A161942(n) / A348992(n).
a(n) = A003961(A349163(n)) = A003961(n/A349164(n)).
(End)
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A342671(n) = gcd(sigma(n), A003961(n));
CROSSREFS
Cf. A000203, A003961, A161942, A286385, A341529, A342672, A342673, A348992, A349161, A349162, A349163, A349164, A349165 (positions of 1's), A349166 (of terms > 1), A349167, A349756, A350071 [= a(n^2)], A355828 (Dirichlet inverse).
Cf. A349169, A349745, A355833, A355924 (applied onto prime shift array A246278).
Sequence in context: A086869 A348953 A095345 * A132468 A353235 A243915
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 20 2021
STATUS
approved