A349168 Numbers k such that sigma(k) and A003961(k) share a prime power divisor that is not a unitary divisor of A003961(k). Here A003961(n) is fully multiplicative function with a(prime(k)) = prime(k+1).

8, 20, 24, 27, 32, 40, 44, 54, 56, 60, 72, 80, 88, 92, 96, 100, 104, 108, 116, 120, 128, 132, 135, 140, 152, 160, 164, 168, 171, 176, 180, 184, 188, 189, 196, 200, 216, 224, 232, 236, 240, 248, 260, 261, 264, 270, 272, 276, 280, 288, 296, 297, 300, 308, 312, 320, 325, 328, 332, 342, 344, 348, 351, 352, 360, 368, 376

Offset

1,1

Comments

Numbers k such that A342671(k) [= gcd(sigma(k), A003961(k)] and A349161(k) [= A003961(k)/A342671(k)] share a prime factor.

Numbers k for which A349163(k) and A349164(k) are not relatively prime.

Links

Table of n, a(n) for n=1..67.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Example

For n = 8 = 2^3, sigma(8) = 15 = 3*5, while A003961(8) = 3^3 = 27. These share the prime power divisor 3, which however is not a unitary divisor of 27, therefore 8 is included in this sequence.
For n = 32 = 2^5, sigma(32) = 63 = 3^2 * 7, while A003961(32) = 3^5 = 243. These share the prime power divisor 3^2, which however is not a unitary divisor of 243, therefore 32 is included.
For n = 40 = 2^3 * 5, sigma(40) = 90 = 2 * 3^2 * 5, while A003961(40) = 3^3 * 7 = 189. These share the prime power divisor 3^2, which however is not a unitary divisor of 189, therefore 40 is included.

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
isA349168(n) = { my(u=A003961(n), x=gcd(u, sigma(n))); (1!=gcd(x, u/x)); };

Crossrefs

Cf. A000203, A003961, A342671, A349161, A349163, A349164.

Subsequence of A349166.

Sequence in context: A205226 A205318 A100212 * A083094 A164916 A207190

Adjacent sequences: A349165 A349166 A349167 * A349169 A349170 A349171

Keyword

nonn

Author

Antti Karttunen, Nov 10 2021

Status

approved