A225757 Table of consecutive numbers with the same sum of divisors.

14, 15, 206, 207, 957, 958, 1334, 1335, 1364, 1365, 1634, 1635, 2685, 2686, 2974, 2975, 4364, 4365, 14841, 14842, 18873, 18874, 19358, 19359, 20145, 20146, 24957, 24958, 33998, 33999, 36566, 36567, 42818, 42819, 56564, 56565, 64665, 64666, 74918, 74919, 79826

Offset

1,1

Comments

Are 3 consecutive terms possible? There are none less than 10^12. See A002961. - T. D. Noe, May 15 2013

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000 (first 226 terms from T. D. Noe)

Example

Sequence begins:
14, 15;
206, 207;
957, 958;
1334, 1335;
etc.

Mathematica

sel = Select[Range[100000], DivisorSigma[1, #] == DivisorSigma[1, # + 1] &]; Union[sel, sel + 1]
Flatten[SequencePosition[DivisorSigma[1, Range[80000]], {x_, x_}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 13 2017 *)

Prog

(PARI) v=List(); t=[1, 3]; for(n=3, 1e6, t=[t[2], sigma(n)]; if(t[1]==t[2], listput(v, n-1); listput(v, n))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, May 15 2013

Crossrefs

Cf. A225756 (same number of divisors), A225758 (same number and sum of divisors), A002961 (first number of each pair).

Sequence in context: A041412 A041414 A033050 * A041416 A041417 A041418

Adjacent sequences: A225754 A225755 A225756 * A225758 A225759 A225760

Keyword

nonn,tabf

Author

Jean-François Alcover, May 15 2013

Status

approved