A350071 a(n) = gcd(sigma(n^2), A003961(n^2)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of divisors function.

1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 7, 1, 1, 13, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 7, 1, 3, 1, 1, 7, 3, 1, 1, 1, 1, 1, 3, 121, 1, 1, 13, 1, 1, 1, 21, 1, 1, 1, 3, 1, 3, 1, 3, 1, 7, 1, 1, 1, 3, 1, 3, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1

Offset

1,10

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) = A342671(n^2).

a(n) = A065764(n) / A350072(n).

Mathematica

f1[p_, e_] := (p^(2*e + 1) - 1)/(p - 1); f2[p_, e_] := NextPrime[p]^(2*e); a[1] = 1; a[n_] := GCD[Times @@ f1 @@@ (f = FactorInteger[n]), Times @@ f2 @@@ f]; Array[a, 100] (* Amiram Eldar, Dec 12 2021 *)

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));
A350071(n) = A342671(n^2);

Crossrefs

Cf. A000203, A000290, A003961, A065764, A350072.

Sequence in context: A351568 A174544 A168423 * A336844 A072101 A366894

Adjacent sequences: A350068 A350069 A350070 * A350072 A350073 A350074

Keyword

nonn

Author

Antti Karttunen, Dec 12 2021

Status

approved