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Numbers m such that there is an integer k with the property that antisigma(m) = k * sigma(m) + k.
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%I #20 Jun 15 2022 01:50:04

%S 1,2,247,2279,9167,57479,200479,518039,2119207,3685439,9240079,

%T 16384279,31536647,101601359,140558807,189771287,299142967,354032447,

%U 384150199,486103279,565468637,802008239,853795074,1107541759,1328438479,1494742004,1580837719,1768013279

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

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

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

%C Numbers m such that sigma(m) + 1 divides antisigma(m). - _Kevin P. Thompson_, Nov 27 2021

%H Kevin P. Thompson, <a href="/A244926/b244926.txt">Table of n, a(n) for n = 1..49</a>

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

%o (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))]

%o (PARI) isok(m) = my(s=sigma(m)); denominator((m*(m+1)/2-s)/(s+1)) == 1; \\ _Michel Marcus_, Jan 21 2022

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

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Jul 08 2014

%E a(10)-a(28) from _Kevin P. Thompson_, Nov 27 2021