A333503 Differences between consecutive odd abundant numbers.

630, 630, 630, 630, 630, 630, 630, 420, 210, 450, 180, 210, 420, 180, 450, 210, 330, 90, 420, 210, 420, 210, 630, 630, 630, 630, 420, 210, 630, 630, 630, 210, 420, 630, 630, 630, 630, 630, 630, 90, 330, 210, 630, 630, 630, 210, 330, 90, 630, 210, 420, 630, 630

Offset: 1

Author

Jeppe Stig Nielsen, Mar 24 2020

Keywords

• nonn

Comments

a(n) = A005231(n+1) - A005231(n).

Since 945+1890*k is odd and abundant for all k, 1890 is the maximal term that occurs. The first time it occurs is for a(274)=1890, and the involved odd abundant numbers are 135135 and 137025.

Clearly 2 is the minimal term that can occur. For an example, see comment to A294025.

Links

• Jeppe Stig Nielsen, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005231, A294025.

Programs

Mathematica

Differences@ Select[Range[947, 3*10^4 + 1, 2], DivisorSigma[1, #] > 2 # &] (* Michael De Vlieger, Mar 25 2020 *)

PARI

my(oldn=945); forstep(n=947, 5*10^4, 2, if(sigma(n)>2*n, print1(n-oldn, ", "); oldn=n))