login
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
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.
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.
Sequence in context: A322903 A363691 A349174 * A323550 A165468 A353124
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 11 2021
STATUS
approved