A101260 Numbers n whose abundance is 56.

84, 140, 224, 308, 364, 476, 532, 644, 812, 868, 1036, 1148, 1204, 1316, 1372, 1484, 1652, 1708, 1876, 1988, 2044, 2212, 2324, 2492, 2716, 2828, 2884, 2996, 3052, 3164, 3556, 3668, 3836, 3892, 4172, 4228, 4396, 4544, 4564, 4676, 4844, 5012, 5068, 5348

Offset

1,1

Comments

If n is of the form p*28, where p is a prime distinct from 2 or 7 then n is in this sequence, note that 28 is a perfect number. The terms in the sequence but not divisible by 28 are 4544, 9272, 14552, 25472, 74992, 495104... - Enrique Pérez Herrero, Apr 15 2012

If p=2^k-57 is prime (cf. A165778), then 2^(k-1)*p is in the sequence: For the first such k=6,7,8,10,16,19,22,28,..., this yields 224, 4544, 25472, 495104, 2145615872, 137424011264, 8795973484544, 36028789368553472, ... - M. F. Hasler, Apr 15 2012

Links

Enrique Pérez Herrero, Table of n, a(n) for n = 1..3000

F. Firoozbakht and M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1.

Example

84 is a term of the sequence because 2*2*3*7 = 84 and 84 - 42 - 28 - 21 - 14 - 12 - 7 - 6 - 4 - 3 - 2 = g(84) = -55.

Mathematica

Select[ Range[5500], DivisorSigma[1, # ] == 2# + 56 &] (* Robert G. Wilson v, Dec 22 2004 *)

Prog

(Magma) [n: n in [1..10^4] |DivisorSigma(1, n) eq 2*n+56]; // Vincenzo Librandi, Jul 30 2015

Crossrefs

Cf. A005101, A033880.

Cf. A141545, A141546.

Sequence in context: A099637 A274348 A143758 * A141502 A039499 A341128

Adjacent sequences: A101257 A101258 A101259 * A101261 A101262 A101263

Keyword

nonn,easy

Author

Vassil K. Tintschev (tinchev(AT)sunhe.jinr.ru), Dec 17 2004

Status

approved