A349175 Odd numbers k for which gcd(k, A003961(k)) <> 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.

15, 27, 35, 45, 57, 65, 75, 77, 87, 99, 105, 143, 165, 171, 175, 177, 189, 195, 205, 221, 225, 231, 237, 245, 255, 261, 267, 297, 301, 315, 323, 325, 327, 345, 351, 375, 385, 399, 405, 415, 417, 429, 437, 447, 459, 465, 485, 495, 513, 525, 531, 537, 539, 555, 567, 585, 595, 597, 605, 609, 615, 621, 627, 629, 645

Offset

1,1

Comments

Odd numbers for which A348994(n) <> A349161(n).

Equally, odd numbers such that A319626(n) <> A349164(n).

Links

Table of n, a(n) for n=1..65.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Mathematica

Select[Range[1, 645, 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); };
isA349175(n) = if(!(n%2), 0, my(u=A003961(n)); gcd(u, sigma(n))!=gcd(u, n));

Crossrefs

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

Cf. A349169, A349174 (complement among the odd numbers).

Sequence in context: A354714 A307854 A053177 * A145195 A096022 A097222

Adjacent sequences: A349172 A349173 A349174 * A349176 A349177 A349178

Keyword

nonn

Author

Antti Karttunen, Nov 10 2021

Status

approved