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A231366 Number of numbers whose sum of non-divisors (A024816) is equal to n. 5
2, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) = frequency of values n in A024816(m), where A024816(m) = sum of non-divisors of m = antisigma(m).

From Charles R Greathouse IV, Nov 11 2013: (Start)

So far all n such that a(n) > 1 correspond to members of A067816:

a(0) = 2 from 1, 2;

a(9) = 2 from 5, 6;

a(36844389) = 2 from 8585, 8586;

a(129894940) = 2 from 16119, 16120;

a(446591224981504) = 2 from 29886159, 29886160.

I checked this, and thus Krizek's conjecture below, up to 4*10^19.

(End)

LINKS

Table of n, a(n) for n=0..86.

FORMULA

Conjecture: max a(n) = 2.

a(A231368(n)) >= 1, a(A231369(n)) = 0.

a(n) = 0 for such n that A231367(n) = 0, a(n) = 0 if A024816(m) = n has no solution.

a(n) >= 1 for such n that A231367(n) = 1, a(n) >= 1 if A024816(m) = n for any m.

Conjecture: a(n) = 2 iff n is number from A225775 (0, 9, 36844389, 129894940, 446591224981504, …)

EXAMPLE

a(9) = 2 because there are two numbers m (5, 6) with antisigma(m) = 9.

CROSSREFS

Cf. A054973 (number of numbers whose divisors sum to n), A231365, A231368, A231367, A231369, A067816.

Sequence in context: A154469 A037273 A285313 * A158924 A025426 A269244

Adjacent sequences:  A231363 A231364 A231365 * A231367 A231368 A231369

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Nov 09 2013

STATUS

approved

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Last modified April 22 10:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)