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a(n) = sum of sigma(e) where e ranges over all non-divisors of n that are between 1 and n.
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%I #9 Oct 28 2024 05:13:03

%S 0,0,3,4,14,13,32,30,51,59,86,72,126,129,154,163,219,205,276,262,326,

%T 355,406,361,484,504,546,561,659,622,761,737,840,883,944,900,1097,

%U 1112,1177,1160,1341,1300,1479,1465,1560,1658,1757,1645,1921,1928,2057,2085

%N a(n) = sum of sigma(e) where e ranges over all non-divisors of n that are between 1 and n.

%H Robert Israel, <a href="/A076663/b076663.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A024916(n) - A007429(n). - _Robert Israel_, Oct 27 2024

%p N:= 1000: # for a(1) .. a(N)

%p S:= [seq(numtheory:-sigma(n),n=1..N)]:

%p SS:= ListTools:-PartialSums(S):

%p seq(SS[n] - add(S[d], d = numtheory:-divisors(n)), n=1..N); # _Robert Israel_, Oct 27 2024

%t f[n_] := Module[{s, i}, s = 0; For[i = 1, i < n, i++, If[Mod[n, i] != 0, s = s + DivisorSigma[1, i]]]; s]; Table[f[i], {i, 1, 100}]

%Y Cf. A000203, A007429, A024916.

%K nonn,changed

%O 1,3

%A _Joseph L. Pe_, Oct 24 2002