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

1,1

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

Prog

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

Crossrefs

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

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

Sequence in context: A028749 A028764 A366319 * A337050 A304364 A336590

Adjacent sequences: A326067 A326068 A326069 * A326071 A326072 A326073

Keyword

nonn

Author

Antti Karttunen, Jun 07 2019

Status

approved