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%I #13 Nov 16 2013 12:01:15
%S 221355126,402640540,668862580,739577140
%N Smallest sets of 8 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.
%C Is this a duplicate of A231093? - _R. J. Mathar_, Nov 15 2013
%C No; there is some element of this sequence not in A231093 below approximately 10^10^72. In fact A228965 \ A231093 has positive lower density (though presumably quite small). Capsule proof: choose n such that an appropriately large number of primes divide n, n+1, ..., n+7. Since the reciprocal of the primes diverges, you can get sigma(n+i)/(n+i) arbitrarily large. - _Charles R Greathouse IV_, Nov 15 2013
%e 221355126, 221355128, 221355130, 221355132, 221355134, 221355136, 221355138, 221355140 is the smallest set of 8 consecutive abundant numbers in arithmetic progression so 221355126 is in the list.
%t AbundantQ[n_] := DivisorSigma[1, n] > 2 n; m = 2; z1 = 18; cd = 6; a = {}; Do[If[AbundantQ[n], If[n - z1 == cd, m = m + 1; If[m > 7, AppendTo[a, n - 7*cd]], m = 2; cd = n - z1]; z1 = n], {n, 19, 1000000000}]; a
%Y Cf. A005101, A228433, A228844, A228961, A228962, A228963, A228964.
%K nonn
%O 1,1
%A _Shyam Sunder Gupta_, Nov 10 2013