A340071 a(n) = gcd(A003961(n)-1, phi(A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes.

1, 2, 4, 2, 6, 2, 10, 2, 4, 4, 12, 4, 16, 4, 2, 2, 18, 2, 22, 2, 2, 2, 28, 2, 6, 2, 4, 2, 30, 8, 36, 2, 16, 4, 4, 8, 40, 4, 4, 4, 42, 4, 46, 4, 6, 2, 52, 4, 10, 2, 2, 8, 58, 2, 18, 4, 2, 4, 60, 2, 66, 2, 2, 2, 2, 2, 70, 2, 16, 10, 72, 2, 78, 2, 4, 2, 2, 2, 82, 2, 4, 4, 88, 2, 12, 4, 2, 2, 96, 4, 2, 4, 8, 2, 4, 2, 100

Offset

1,2

Comments

Prime shifted analog of A049559.

Links

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

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A049559(A003961(n)).

a(n) = gcd(A253885(n-1), A003972(n)) = gcd(A003961(n)-1, A000010(A003961(n))).

a(n) = A003972(n) / A340072(n).

For n > 1, a(n) = (A003961(n)-1) / A340073(n).

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A340071(n) = { my(u=A003961(n)); gcd(u-1, eulerphi(u)); };

Crossrefs

Cf. A000010, A003961, A003972, A049559, A253885, A340072, A340073.

Cf. also A340081.

Sequence in context: A212122 A213372 A286601 * A102128 A181980 A230436

Adjacent sequences: A340068 A340069 A340070 * A340072 A340073 A340074

Keyword

nonn

Author

Antti Karttunen, Dec 28 2020

Status

approved