A228965 Smallest sets of 8 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.

221355126, 402640540, 668862580, 739577140

Offset: 1

Author

Shyam Sunder Gupta, Nov 10 2013

Keywords

• nonn

Comments

Is this a duplicate of A231093? - R. J. Mathar, Nov 15 2013

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

Examples

			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.
		

Crossrefs

Cf. A005101, A228433, A228844, A228961, A228962, A228963, A228964.

Programs

Mathematica

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