

A101260


Numbers n whose abundance is 56.


2



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
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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^k57 is prime (cf. A165778), then 2^(k1)*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



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



KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



