cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

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Author

Altug Alkan, Jul 25 2016

Keywords

Comments

The smallest term that is not divisible by 5 is 1577106531.

Examples

			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.
		

Crossrefs

Programs

  • PARI
    isok(n) = sigma(n) == sigma(2*n-1) && n % 2 == 1

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

Views

Author

Altug Alkan, Aug 01 2017

Keywords

Comments

46495995 = 3*5*7*13*23*1481 is the smallest odd term of this sequence.

Crossrefs

Programs

  • Mathematica
    usigma[1] = 1;  usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); Select[Range[10^5], usigma[#] == usigma[2#+1] &] (* Amiram Eldar, Aug 04 2019 *)
  • PARI
    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

Views

Author

K. D. Bajpai, Jul 10 2017

Keywords

Comments

Most of the terms in this sequence are even.
Up to 10^7 there are 102 terms out of which 7 are odd.
There are two terms, 6 and 496, for which (2*k - 1) is a prime number.

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).
		

Crossrefs

Cf. A000203, A005101, A272553, A275370 (odd terms).

Programs

  • Magma
    [n : n in [1..10^6] | SumOfDivisors(n) eq SumOfDivisors(2*n-1)];
  • Maple
    with(numtheory): select(t -> sigma(t) = sigma(2*t-1), [$1..10^6]);
  • Mathematica
    Select[Range[10^7], DivisorSigma[1, #] == DivisorSigma[1, 2 # - 1] &]
  • PARI
    for (n = 1,  1e7, (sigma(n)==sigma(2*n-1)) && print1(n ", "));
    
Showing 1-3 of 3 results.