A244926 Numbers m such that there is an integer k with the property that antisigma(m) = k * sigma(m) + k.

1, 2, 247, 2279, 9167, 57479, 200479, 518039, 2119207, 3685439, 9240079, 16384279, 31536647, 101601359, 140558807, 189771287, 299142967, 354032447, 384150199, 486103279, 565468637, 802008239, 853795074, 1107541759, 1328438479, 1494742004, 1580837719, 1768013279

Offset: 1

Author

Jaroslav Krizek, Jul 08 2014

Keywords

• nonn

Comments

Numbers m such that A244329(m) = floor(antisigma(m) / sigma(m)) = antisigma(m) mod sigma(m) = A232324(n).

Corresponding values of integers k: 0, 0, 108, 1092, 4488, 28500, 99792, 258300, 1058148, ...

Numbers m such that sigma(m) + 1 divides antisigma(m). - Kevin P. Thompson, Nov 27 2021

Examples

			247 is in sequence because 30348 = antisigma(247) = 108 * sigma(247) + 108 = 108*280 + 108.
		

Links

• Kevin P. Thompson, Table of n, a(n) for n = 1..49

Crossrefs

Cf. A024816 (antisigma), A000203 (sigma), A244329, A232324.

Programs

Magma

[n: n in [1..100000] | Floor(((n*(n+1)div 2) - (SumOfDivisors(n))) div (SumOfDivisors(n))) eq ((n*(n+1)div 2) - (SumOfDivisors(n))) mod (SumOfDivisors(n))]

PARI

isok(m) = my(s=sigma(m)); denominator((m*(m+1)/2-s)/(s+1)) == 1; \\ Michel Marcus, Jan 21 2022

Extensions

a(10)-a(28) from Kevin P. Thompson, Nov 27 2021