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

1,2

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

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).

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] &]

Prog

(PARI) for (n = 1,  1e7, (sigma(n)==sigma(2*n-1)) && print1(n ", "));
(Magma) [n : n in [1..10^6] | SumOfDivisors(n) eq SumOfDivisors(2*n-1)];

Crossrefs

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

Sequence in context: A212490 A047941 A229501 * A211089 A221923 A000409

Adjacent sequences: A289735 A289736 A289737 * A289739 A289740 A289741

Keyword

nonn

Author

K. D. Bajpai, Jul 10 2017

Status

approved