A352810 Values taken both by sigma (A000203) and by antisigma (A024816), where sigma is the sum of divisors function and antisigma is the sum of the non-divisors of n less than n function.

3, 20, 32, 54, 96, 132, 168, 217, 240, 252, 294, 338, 350, 464, 465, 582, 819, 1052, 1080, 1182, 1280, 1476, 1710, 1953, 2220, 2484, 2786, 3080, 3200, 3402, 3708, 4074, 4404, 4440, 4680, 4794, 5250, 5670, 6064, 6080, 6576, 6900, 7248, 7458, 8000, 8442, 8514, 8940

Offset

1,1

Comments

Common values attained by sigma and antisigma functions, in ascending order.

The asymptotic density of this sequence is 0 (according to 2nd comment of A002191).

The smallest integers k and m such that sigma(k) = antisigma(m) = a(n) are in A352811.

Links

Table of n, a(n) for n=1..48.

Example

As sigma(31) = 1+31 = 32 and antisigma(9) = 1+2+4+5+6+7+8 = 32, then 32 is a term.

Mathematica

m = 10^4; r = Range[m]; s = DivisorSigma[1, r]; as = r*(r + 1)/2 - s; Select[Intersection[s, as], # <= m &] (* Amiram Eldar, Apr 05 2022 *)

Crossrefs

Intersection of A002191 and A231365.

Cf. A000203, A024816, A352811.

Sequence in context: A053748 A372976 A075358 * A002461 A254501 A031106

Adjacent sequences: A352807 A352808 A352809 * A352811 A352812 A352813

Keyword

nonn

Author

Bernard Schott, Apr 04 2022

Extensions

More terms from Amiram Eldar, Apr 05 2022

Status

approved