A349174 Odd numbers k for which gcd(k, A003961(k)) is equal to gcd(sigma(k), A003961(k)), 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, 135, 137, 139, 141, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 167, 169

Offset: 1

Author

Antti Karttunen, Nov 10 2021

Keywords

• nonn

Comments

Odd numbers k for which A322361(k) = A342671(k).

Odd numbers k for which A348994(k) = A349161(k).

Odd numbers k such that A319626(k) = A349164(k).

Odd terms of A336702 form a subsequence of this sequence. See also A349169.

Ratio of odd numbers residing in this sequence, vs. in A349175 seems to slowly decrease, but still apparently stays > 2 for a long time. E.g., for range 2 .. 2^28, it is 95302074/38915653 = 2.4489...

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A319626, A322361, A336702, A342671, A348994, A349161, A349164, A349169.

Cf. A349175 (complement among the odd numbers).

Union of A349176 and A349177.

Programs

Mathematica

Select[Range[1, 169, 2], GCD[#1, #3] == GCD[#2, #3] & @@ {#, DivisorSigma[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); };
isA349174(n) = if(!(n%2),0,my(u=A003961(n)); gcd(u,sigma(n))==gcd(u,n));