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

Author

Antti Karttunen, Nov 11 2021

Keywords

• nonn

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

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

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

Complement of A349168.

Cf. A349165 (subsequence).

Programs

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 *)

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)); };