A231090 Initial members of abundant sextuplets, i.e., values of n such that (n, n+2, n+4, n+6, n+8, n+10) are all abundant numbers.
801340, 962650, 7353340, 21964300, 41642140, 48049690, 55455940, 89034940, 89851450, 92253850, 105259540, 107948380, 109455340, 114295450, 116754940, 122349370, 135575980, 156009850, 159521050, 173645440, 188586700, 192674170, 193137850, 220301770, 221355126
Offset: 1
Keywords
Examples
801340, 801342, 801344, 801346, 801348, 801350 are abundant, thus the smallest number is listed.
Links
- Shyam Sunder Gupta and Donovan Johnson, Table of n, a(n) for n = 1..5000 (first 126 terms from Shyam Sunder Gupta)
Programs
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Mathematica
AbundantQ[n_] := DivisorSigma[1, n] > 2n; m = 0; a = {}; Do[If[AbundantQ[n], m = m + 1; If[m > 5, AppendTo[a, n - 10]], m = 0], {n, 2, 1000000000, 2}];a 2*SequencePosition[Table[If[DivisorSigma[1,n]>2n,1,0],{n,2,2214*10^5,2}],{1,1,1,1,1,1}][[All,1]] (* Harvey P. Dale, May 12 2022 *) -
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 \\ Charles R Greathouse IV, Feb 21 2017