A096536 Numbers k such that k, k+1, k+2 are all abundant.

171078830, 268005374, 321893648, 336038624, 487389824, 600350750, 663249950, 668645054, 938109248, 1053424448, 1079741024, 1102433408, 1139364224, 1148927624, 1267293950, 1275861950, 1310259950, 1344330350, 1352253824

Offset

1,1

Comments

The entries shown are all even, the first odd k would have to have sigma(k*(k+2)) > 4k*(k+2) so k > 10^19 (cf. A119240).

From Amiram Eldar, Oct 02 2022: (Start)

The least term that is == 1 (mod 3) is a(1292) = 55959128224, and the least term that is divisible by 3 is a(1590) = 68972878974.

The numbers of terms not exceeding 10^k, for k = 9, 10, ..., are 9, 226, 2298, 22583, ... . Apparently, the asymptotic density of this sequence exists and equals 2.2...*10^(-8). (End)

Links

Amiram Eldar, Table of n, a(n) for n = 1..22583 (terms below 10^12; terms 1..1000 from Donovan Johnson)

Carlos Rivera, Puzzle 878. Consecutive abundant integers, The Prime Puzzles & Problems Connection.

Carlos Rivera, Puzzle 880. Consecutive odd abundant integers, The Prime Puzzles & Problems Connection.

Example

For 171078830 = 2*5*13*23*29*1973, sigma(n)/n = 2.09355, for 171078831 = 3^3*7*11*19*61*71, sigma(n)/n = 2.00396 and for 171078832 = 2^4*31*344917, sigma(n)/n = 2.00000579.

Prog

(PARI) isab(x) = sigma(x) > 2*x; \\ A005101
isok(k) = isab(k) && isab(k+1) && isab(k+2); \\ Michel Marcus, Nov 19 2022

Crossrefs

Subsequence of A005101 and A096399.

Cf. A119240.

Sequence in context: A250934 A233606 A258956 * A104331 A233598 A187316

Adjacent sequences: A096533 A096534 A096535 * A096537 A096538 A096539

Keyword

nonn

Author

John L. Drost, Aug 13 2004

Extensions

a(15)-a(19) from Donovan Johnson, Dec 29 2008

Status

approved