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

Author

Shyam Sunder Gupta, Nov 03 2013

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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