A349144 Numbers k for which A342671(k) [= gcd(sigma(k), A003961(k))] and A349161(k) [= A003961(k)/A342671(k)] are relatively prime, where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 93, 94, 95

Offset

1,2

Comments

Numbers k for which A349163(k) and A349164(k) are coprime, i.e., k such that A349163(k) and A349164(k) are unitary divisors of k.

Links

Table of n, a(n) for n=1..81.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Mathematica

Select[Range[95], GCD[#2, #1/#2] == 1 & @@ {#2, #2/GCD[##]} & @@ {DivisorSigma[1, #], If[# == 1, 1, Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]]} &] (* Michael De Vlieger, Nov 11 2021 *)

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
isA349144(n) = { my(u=A003961(n), x=gcd(u, sigma(n))); (1==gcd(x, u/x)); };

Crossrefs

Cf. A000203, A003961, A342671, A349161, A349163, A349164.

Complement of A349168.

Cf. A349165 (subsequence).

Sequence in context: A183220 A187947 A242094 * A171524 A052421 A248375

Adjacent sequences: A349141 A349142 A349143 * A349145 A349146 A349147

Keyword

nonn

Author

Antti Karttunen, Nov 11 2021

Status

approved