

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
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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

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


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



