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 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. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 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 *) PROG (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)); CROSSREFS Cf. A000203, A003961, A319626, A322361, A336702, A342671, A348994, A349161, A349164, A349169. Cf. A349175 (complement among the odd numbers). Union of A349176 and A349177. Sequence in context: A318978 A327755 A322903 * A349177 A323550 A165468 Adjacent sequences:  A349171 A349172 A349173 * A349175 A349176 A349177 KEYWORD nonn AUTHOR Antti Karttunen, Nov 10 2021 STATUS approved

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Last modified September 28 17:45 EDT 2022. Contains 357080 sequences. (Running on oeis4.)