A289738 Numbers k whose sum of divisors equals the sum of divisors of 2*k-1.
1, 6, 348, 496, 1420, 1854, 4674, 5352, 6424, 13545, 21126, 28210, 37336, 57645, 84370, 95526, 109648, 116865, 140056, 150366, 163450, 176826, 215430, 305900, 321496, 330858, 517914, 558304, 590790, 617260, 682746, 742518, 888550, 927336, 952938, 1058344, 1096758
Offset: 1
Keywords
Examples
6 is in the sequence because the sum of divisors of 6: (1 + 2 + 3 + 6 = 12); equals the sum of divisors of 11 = 2*6 - 1: (1 + 11 = 12). 348 is in the sequence because the sum of divisors of 348: (1 + 2 + 3 + 4 + 6 + 12 + 29 + 58 + 87 + 116 + 174 + 348 = 840); equals the sum of divisors of (2*348 - 1 = 695): (1 + 5 + 139 + 695 = 840).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1000
Programs
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Magma
[n : n in [1..10^6] | SumOfDivisors(n) eq SumOfDivisors(2*n-1)];
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Maple
with(numtheory): select(t -> sigma(t) = sigma(2*t-1), [$1..10^6]);
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Mathematica
Select[Range[10^7], DivisorSigma[1, #] == DivisorSigma[1, 2 # - 1] &]
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PARI
for (n = 1, 1e7, (sigma(n)==sigma(2*n-1)) && print1(n ", "));
Comments