A323072 -id:A323072 - cp's OEIS frontend

A323071 a(n) = gcd(n, 1+A060681(n)).

1, 2, 3, 1, 5, 2, 7, 1, 1, 2, 11, 1, 13, 2, 1, 1, 17, 2, 19, 1, 3, 2, 23, 1, 1, 2, 1, 1, 29, 2, 31, 1, 1, 2, 1, 1, 37, 2, 3, 1, 41, 2, 43, 1, 1, 2, 47, 1, 1, 2, 1, 1, 53, 2, 5, 1, 3, 2, 59, 1, 61, 2, 1, 1, 1, 2, 67, 1, 1, 2, 71, 1, 73, 2, 3, 1, 1, 2, 79, 1, 1, 2, 83, 1, 1, 2, 1, 1, 89, 2, 1, 1, 3, 2, 1, 1, 97, 2, 1, 1, 101, 2, 103, 1, 1

Offset: 1

Antti Karttunen, Jan 04 2019

nonn

Differs from A055023 at n = 55, 105, 155, ..., (A323070).

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Cf. A055023, A060681, A323070, A323072.

A060681(n) = (n-if(1==n,n,n/vecmin(factor(n)[,1])));
A323071(n) = gcd(n,1+A060681(n));

a(n) = gcd(n, 1+A060681(n)).

a(n) = n/A323072(n).

A340079 a(n) = n / gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).

Original entry on oeis.org

1, 1, 1, 4, 1, 3, 1, 8, 9, 5, 1, 12, 1, 7, 15, 16, 1, 9, 1, 20, 7, 11, 1, 24, 25, 13, 27, 4, 1, 15, 1, 32, 33, 17, 35, 36, 1, 19, 13, 40, 1, 3, 1, 44, 9, 23, 1, 48, 49, 25, 51, 52, 1, 27, 11, 56, 19, 29, 1, 60, 1, 31, 63, 64, 65, 33, 1, 68, 69, 35, 1, 72, 1, 37, 75, 76, 77, 39, 1, 80, 81, 41, 1, 84, 85, 43, 87, 88

Offset: 1

Antti Karttunen, Dec 30 2020

nonn

It is conjectured that this is 1 iff n is 1 or a prime. See Thomas Ordowski's Oct 22 2014 comment in A018804.

Antti Karttunen, Table of n, a(n) for n = 1..8191
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A018804, A340078, A340080.

Cf. also A055032, A323072 (similar but different sequences).

A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
A340079(n) = (n/gcd(n,1+A018804(n)));

a(n) = n / A340078(n) = n / gcd(n, 1+A018804(n)).

A323070 Numbers k such that A055023(k) != A323071(k), where A323071(k) = gcd(k, 1+A060681(k)).

Original entry on oeis.org

55, 105, 155, 203, 253, 355, 405, 455, 497, 595, 655, 689, 705, 737, 755, 791, 955, 979, 1005, 1027, 1055, 1081, 1221, 1255, 1305, 1355, 1379, 1555, 1605, 1655, 1673, 1703, 1711, 1751, 1855, 1905, 1955, 1967, 2065, 2155, 2189, 2205, 2255, 2261, 2329, 2455, 2505, 2555, 2755, 2805, 2849, 2855, 3055

Offset: 1

Antti Karttunen, Jan 04 2019

nonn

Equivalently, numbers k for which A055032(k) != A323072(k).

Neither primes nor prime powers present?

Cf. A055023, A055032, A060681, A323071, A323072.

A055023(n) = (n/denominator((sum(m=1, n - 1, m^(n - 1)) + 1)/n)); \\ From A055023.
A060681(n) = (n-if(1==n,n,n/vecmin(factor(n)[,1])));
A323071(n) = gcd(n,1+A060681(n));
is_A323070(n) = (A055023(n)!=A323071(n));

A339913 a(n) = x/gcd(n,x), where x = 1+A060681(n).

Original entry on oeis.org

1, 1, 1, 3, 1, 2, 1, 5, 7, 3, 1, 7, 1, 4, 11, 9, 1, 5, 1, 11, 5, 6, 1, 13, 21, 7, 19, 15, 1, 8, 1, 17, 23, 9, 29, 19, 1, 10, 9, 21, 1, 11, 1, 23, 31, 12, 1, 25, 43, 13, 35, 27, 1, 14, 9, 29, 13, 15, 1, 31, 1, 16, 43, 33, 53, 17, 1, 35, 47, 18, 1, 37, 1, 19, 17, 39, 67, 20, 1, 41, 55, 21, 1, 43, 69, 22, 59, 45, 1, 23

Offset: 1

Antti Karttunen, Jan 01 2021

nonn

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

Cf. A060681, A323071, A323072.

A060681(n) = (n-if(1==n,n,n/vecmin(factor(n)[,1])));
A339913(n) = { my(x=1+A060681(n)); (x/gcd(n,x)); };

a(n) = (1+A060681(n)) / A323071(n).

cp's OEIS Frontend

A323071 a(n) = gcd(n, 1+A060681(n)).

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A340079 a(n) = n / gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).

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A323070 Numbers k such that A055023(k) != A323071(k), where A323071(k) = gcd(k, 1+A060681(k)).

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PARI

A339913 a(n) = x/gcd(n,x), where x = 1+A060681(n).

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