A349176 Odd numbers k for which gcd(k, A003961(k)) = gcd(sigma(k), A003961(k)) > 1, where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.

135, 285, 435, 455, 855, 885, 1185, 1287, 1305, 1335, 1425, 1435, 1485, 1635, 2235, 2275, 2295, 2655, 2685, 2905, 2985, 3105, 3135, 3185, 3311, 3395, 3435, 3555, 3585, 4005, 4035, 4185, 4425, 4785, 4865, 4905, 4995, 5385, 5685, 5805, 5835, 5845, 5925, 6135, 6237, 6335, 6345, 6585, 6675, 6735, 7125, 7155, 7175, 7185

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Example

For n = 135 = 3^3 * 5, sigma(135) = 240 = 2^4 * 3 * 5, A003961(135) = 5^3 * 7 = 875, and gcd(135,875) = gcd(240,875) = 5, which is larger than 1, therefore 135 is included in the sequence.

Mathematica

Select[Range[1, 7200, 2], And[#1/#2 == #1/#3, #2 > 1] & @@ {#3, 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); };
isA349176(n) = if(!(n%2), 0, my(u=A003961(n), t=gcd(u, n)); (t>1)&&(gcd(u, sigma(n))==t));

Crossrefs

Intersection of A104210 and A349174, or equally, intersection of A349166 and A349174.

Subsequence of A372567.

Cf. A000203, A003961, A319626, A348994, A349161, A349164, A349169.

Sequence in context: A274434 A325569 A372567 * A342189 A374461 A176313

Adjacent sequences: A349173 A349174 A349175 * A349177 A349178 A349179

Keyword

nonn

Author

Antti Karttunen, Nov 11 2021

Status

approved