A349177 Odd numbers k for which gcd(k, A003961(k)) = gcd(sigma(k), A003961(k)) = 1, where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.

1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 29, 31, 33, 37, 39, 41, 43, 47, 49, 51, 53, 55, 59, 61, 63, 67, 69, 71, 73, 79, 81, 83, 85, 89, 91, 93, 95, 97, 101, 103, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 137, 139, 141, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 167, 169, 173

Offset

1,2

Comments

Odd numbers k for which k and A003961(k) are relatively prime, and also sigma(k) and A003961(k) are coprime.

Links

Table of n, a(n) for n=1..72.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Mathematica

Select[Range[1, 173, 2], GCD[#1, #3] == GCD[#2, #3] == 1 & @@ {#, DivisorSigma[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); };
isA349177(n) = if(!(n%2), 0, my(u=A003961(n), t=gcd(u, n)); (1==t)&&(gcd(u, sigma(n))==t));

Crossrefs

Subsequence of A349174 from this first differs by not having term 135 (see A349176).

Intersection of A319630 and A349174, or equally, intersection of A349165 and A349174.

Cf. A000203, A003961, A319626, A348994, A349161, A349164, A349169.

Sequence in context: A322903 A363691 A349174 * A323550 A165468 A353124

Adjacent sequences: A349174 A349175 A349176 * A349178 A349179 A349180

Keyword

nonn

Author

Antti Karttunen, Nov 11 2021

Status

approved