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Numbers n such that sigma(n) mod n - antisigma(n) mod n = 14, where sigma(n) = A000203(n) = sum of divisor of n, antisigma(n) = A024816(n) = sum of non-divisors of n.
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%I #13 Nov 02 2013 02:40:47

%S 32,44,52,68,76,92,116,124,144,148,164,172,188,212,236,244,268,284,

%T 292,316,332,356,388,404,412,428,436,452,508,524,548,556,596,604,628,

%U 652,668,692,716,724,764,772,788,796,844,892,908,916,932,956,964,1004,1028

%N Numbers n such that sigma(n) mod n - antisigma(n) mod n = 14, where sigma(n) = A000203(n) = sum of divisor of n, antisigma(n) = A024816(n) = sum of non-divisors of n.

%C Numbers n such that A229087(n) = A000203(n) mod n - A024816(n) mod n = A054024(n) - A229110(n) = 14.

%C Value 14 has in sequence A229087(n) anomalous increased frequency.

%C Subsequence of A229090 (numbers n such that sigma(n) mod n > antisigma(n) mod n).

%H Jaroslav Krizek, <a href="/A229115/b229115.txt">Table of n, a(n) for n = 1..2761 (all terms < 10^5)</a>

%e Number 32 is in sequence because sigma(32) mod 32 - antisigma(32) mod 32 = 63 mod 32 - 465 mod 32 = 31 - 17 = 14.

%o (PARI) isok(n) = ((sigma(n) % n) - (n*(n+1)/2 - sigma(n)) % n) == 14; \\ _Michel Marcus_, Oct 31 2013

%Y Cf. A000203 (sigma(n)), A024816 (antisigma(n)), A229110 (antisigma(n) mod n), A054024 (sigma(n) mod n), A229090.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Oct 24 2013