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A355932
a(n) = gcd(sigma(n), sigma(A003961(n))), where A003961 is fully multiplicative with a(p) = nextprime(p).
4
1, 1, 2, 1, 2, 12, 4, 5, 1, 2, 2, 2, 2, 24, 24, 1, 2, 1, 4, 2, 8, 4, 6, 60, 1, 6, 4, 4, 2, 24, 2, 7, 12, 2, 48, 13, 2, 12, 4, 10, 2, 96, 4, 14, 2, 24, 6, 2, 19, 3, 24, 2, 6, 24, 8, 120, 16, 2, 2, 24, 2, 8, 4, 1, 12, 48, 4, 2, 12, 48, 2, 5, 2, 6, 2, 4, 24, 24, 4, 2, 11, 2, 6, 8, 4, 12, 24, 20, 2, 2, 8, 6, 4, 72, 24
OFFSET
1,3
FORMULA
a(n) = gcd(A000203(n), A003973(n)).
a(n) = A003973(n) / A355933(n).
a(n) = A000203(n) / A355934(n).
MATHEMATICA
f[p_, e_] := ((q = NextPrime[p])^(e + 1) - 1)/(q - 1); a[1] = 1; a[n_] := GCD[DivisorSigma[1, n], Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, Jul 22 2022 *)
PROG
(PARI)
A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
A355932(n) = gcd(sigma(n), A003973(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 22 2022
STATUS
approved