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

Author

Antti Karttunen, Nov 10 2021

Keywords

• nonn

Comments

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

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

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

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

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

Programs

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 *)

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));