A231092 Initial members of abundant septuplets, i.e., values of n such that (n, n+2, n+4, n+6, n+8, n+10, n+12) are all abundant numbers.

221355126, 221355128, 402640540, 402640542, 668862580, 668862582, 739577140, 739577142, 1415514246, 1415514248, 1598558646, 1598558648, 1678915540, 1678915542, 1714512246, 1714512248, 1812156340, 1812156342, 1829740086, 1829740088, 1892686326, 1892686328

Offset

1,1

Comments

If the terms are divided into groups of two, are the differences between the two grouped terms always 2? - Harvey P. Dale, Mar 24 2025

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Example

221355126, 221355128, 221355130, 221355132, 221355134, 221355136, 221355138 are abundant, thus the smallest number is listed.

Mathematica

AbundantQ[n_] := DivisorSigma[1, n] > 2n; m = 0; a = {}; Do[If[AbundantQ[n], m = m + 1; If[m > 6, AppendTo[a, n - 12]], m = 0], {n, 2, 2000000000, 2}]; a
SequencePosition[Table[If[DivisorSigma[1, n]>2n, 1, 0], {n, 18927*10^5}], {1, _, 1, _, 1, _, 1, _, 1, _, 1, _, 1}][[;; , 1]] (* Harvey P. Dale, Mar 24 2025 *)

Prog

(PARI) is(n)=sigma(n, -1)>2 && sigma(n+2, -1)>2 && sigma(n+4, -1)>2 && sigma(n+6, -1)>2 && sigma(n+8, -1)>2 && sigma(n+10, -1)>2 && sigma(n+12, -1)>2 \\ Charles R Greathouse IV, Feb 21 2017

Crossrefs

Cf. A005101, A108926, A231086, A231088, A231089, A231090, A231093.

Sequence in context: A268313 A268314 A231630 * A228965 A231093 A262559

Adjacent sequences: A231089 A231090 A231091 * A231093 A231094 A231095

Keyword

nonn

Author

Shyam Sunder Gupta, Nov 03 2013

Status

approved