A275370
Odd numbers n such that sigma(n) = sigma(2*n-1).
Original entry on oeis.org
1, 13545, 57645, 116865, 1440495, 7029855, 8596455, 27361125, 41100345, 48289185, 56122185, 77560065, 103225185, 134813385, 146591235, 163817745, 188358885, 198748305, 242668335, 269436375, 352094715, 358841385, 535135965, 563911335, 636719265, 712457655, 724692045
Offset: 1
The numbers n that solve sigma(n) = sigma(2n-1) are n = 1, 6, 348, 496, 1420, 1854, 4647, 5352, 6424, 13545, 21126,... The sequence selects the odd members.
A286837
Numbers n such that usigma(n) = usigma(2*n+1) where usigma(n) = A034448(n).
Original entry on oeis.org
1386, 6790, 8130, 18618, 21378, 27654, 38874, 60030, 64020, 71058, 89178, 92130, 97014, 117114, 118902, 180438, 182226, 224058, 247044, 396078, 495114, 510906, 528510, 723486, 855966, 979098, 1007562, 1012380, 1032360, 1141194, 1302906, 1410294
Offset: 1
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usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); Select[Range[10^5], usigma[#] == usigma[2#+1] &] (* Amiram Eldar, Aug 04 2019 *)
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a034448(n) = sumdivmult(n, d, if(gcd(d, n/d)==1, d));
isok(n) = a034448(n)==a034448(2*n+1); \\ after Charles R Greathouse IV at A034448
A289738
Numbers k whose sum of divisors equals the sum of divisors of 2*k-1.
Original entry on oeis.org
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
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).
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[n : n in [1..10^6] | SumOfDivisors(n) eq SumOfDivisors(2*n-1)];
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with(numtheory): select(t -> sigma(t) = sigma(2*t-1), [$1..10^6]);
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Select[Range[10^7], DivisorSigma[1, #] == DivisorSigma[1, 2 # - 1] &]
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for (n = 1, 1e7, (sigma(n)==sigma(2*n-1)) && print1(n ", "));
Showing 1-3 of 3 results.
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