A179626 Distance between the n-th abundant number and the nearest prime below it.

1, 1, 1, 1, 1, 5, 3, 1, 1, 1, 3, 1, 5, 3, 1, 5, 1, 1, 5, 1, 7, 3, 1, 1, 1, 3, 1, 7, 13, 1, 1, 1, 5, 1, 5, 3, 5, 1, 1, 3, 1, 5, 1, 3, 1, 1, 5, 9, 11, 5, 9, 11, 1, 1, 1, 1, 5, 1, 1, 3, 1, 1, 1, 5, 3, 1, 5, 1, 7, 11, 13, 1, 1, 1, 3, 7, 13, 5, 3, 5, 1, 1, 3, 1, 1, 5, 7, 1, 5, 5, 1, 1, 1, 3, 7, 3, 1, 7, 5, 7, 1, 5, 1

Offset

1,6

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The first abundant number is 12. The nearest prime less than 12 is 11, so a(1) = 12 - 11 = 1. Similarly, the sixth abundant number is 36. The nearest prime less than 36 is 31, so a(6) = 36 - 31= 5.

Mathematica

fQ[n_] := DivisorSigma[1, n] > 2 n; f[n_] := n - NextPrime[n, -1]; f@# & /@ Select[ Range@ 450, fQ] (* Robert G. Wilson v, Jul 23 2010 *)
#-NextPrime[#, -1]&/@(Select[Range[500], DivisorSigma[1, #]>2#&]) (* Harvey P. Dale, May 21 2018 *)

Crossrefs

Cf. A005101, A000040.

Sequence in context: A368602 A132199 A111142 * A174965 A159671 A094853

Adjacent sequences: A179623 A179624 A179625 * A179627 A179628 A179629

Keyword

nonn

Author

Jason G. Wurtzel, Jul 21 2010

Extensions

a(15) onwards from Robert G. Wilson v, Jul 23 2010

Status

approved