A181647 Numbers m having the same sum of divisors as m+20 has.

42, 51, 123, 141, 204, 371, 497, 708, 923, 992, 1034, 1343, 1391, 1484, 1595, 1691, 1826, 3266, 3317, 5015, 5152, 7367, 8003, 9132, 9287, 9494, 11078, 13223, 15458, 15833, 17975, 18752, 19428, 20120, 20915, 21251, 21566, 24119, 24503, 25787, 28000, 29726, 29795

Offset

1,1

References

Jean-Marie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, page 16.

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 100 terms from Reinhard Zumkeller)

Andreas Weingartner, On the Solutions of sigma(n) = sigma(n+k), Journal of Integer Sequences, Vol. 14 (2011), Article 11.5.5.

Formula

A000203(a(n)) = A000203(a(n) + 20).

Example

a(1) = 42, divisors(42) = {1,2,3,6,7,14,21,42}, divisors(42+20) = {1,2,31,62}: 1+2+3+6+7+14+21+42 = 1+2+31+62.

Mathematica

Select[Range[30000], Equal @@ DivisorSigma[1, # + {0, 20}] &] (* Amiram Eldar, Apr 16 2025 *)

Prog

(PARI) isok(n) = sigma(n) == sigma(n+20); \\ Michel Marcus, Feb 06 2016

Crossrefs

Cf. A000203, A002961, A007373, A015861, A015863, A015865, A015866, A015867, A015876, A015877, A015880, A015881, A015882, A015883.

Sequence in context: A390319 A255513 A186456 * A105346 A108119 A175103

Adjacent sequences: A181644 A181645 A181646 * A181648 A181649 A181650

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2010

Status

approved