A355934 a(n) = sigma(n) / gcd(sigma(n), sigma(A003961(n))), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.

1, 3, 2, 7, 3, 1, 2, 3, 13, 9, 6, 14, 7, 1, 1, 31, 9, 39, 5, 21, 4, 9, 4, 1, 31, 7, 10, 14, 15, 3, 16, 9, 4, 27, 1, 7, 19, 5, 14, 9, 21, 1, 11, 6, 39, 3, 8, 62, 3, 31, 3, 49, 9, 5, 9, 1, 5, 45, 30, 7, 31, 12, 26, 127, 7, 3, 17, 63, 8, 3, 36, 39, 37, 19, 62, 35, 4, 7, 20, 93, 11, 63, 14, 28, 27, 11, 5, 9, 45, 117

Offset

1,2

Comments

Denominator of ratio A003973(n) / A000203(n). See comments in A355933.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A000203(n) / A355932(n) = A000203(n) / gcd(A000203(n), A003973(n)).

Mathematica

f[p_, e_] := ((q = NextPrime[p])^(e + 1) - 1)/(q - 1); a[1] = 1; a[n_] := Denominator[Times @@ f @@@ FactorInteger[n] / DivisorSigma[1, 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)); };
A355934(n) = { my(u=sigma(n)); (u/gcd(A003973(n), u)); };

Crossrefs

Cf. A000203, A003961, A003973, A355932, A355933 (numerators), A355940, A355941 (positions of 1's).

Cf. also A336849, A349162.

Sequence in context: A266664 A308439 A245601 * A296513 A099378 A182885

Adjacent sequences: A355931 A355932 A355933 * A355935 A355936 A355937

Keyword

nonn,frac

Author

Antti Karttunen, Jul 22 2022

Status

approved