A326070 Numbers k such that A325977(k) has the same sign as A325978(k).

2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 100

Offset: 1

Author

Antti Karttunen, Jun 07 2019

Keywords

• nonn

Comments

Here A325977(k) = A325973(k) - k and A325978(k) = k - A325974(k), where A325973(k) is the average of {sum of unitary divisors} and {sum of squarefree divisors} = (1/2) * (A034448(k) + A048250(k)) while A325974(k) is the average of {sum of non-unitary divisors} and {sum of nonsquarefree divisors} = (1/2)*(A048146(k) + A162296(k)). Only if signs of A325977(k) and A325978(k) are equal can their difference A325978(k) - A325977(k) = (k - A325974(k)) - (A325973(k) - k) = 2k - (A325973(k) + A325974(k)) = 2k - A000203(k) = A033879(k) be zero, which happens when k is a perfect number (in A000396).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A033879, A325963, A325973, A325974, A325975, A325977, A325978, A325981.

Cf. A326071 (complement), A326072, A000396 (a subsequence).

Programs

PARI

isA326070(n) = (sign(A325977(n))==sign(A325978(n))); \\ For other needed code, see under A325975.