A077374
Odd numbers m whose abundance by absolute value is at most 10, that is, -10 <= sigma(m) - 2m <= 10.
Original entry on oeis.org
1, 3, 5, 7, 9, 11, 15, 21, 315, 1155, 8925, 32445, 442365, 815634435
Offset: 1
sigma(32445) = 64896 and 32445*2 = 64890, which makes the odd number 32445 six away from perfection: A(32445) = 6 and hence in this sequence.
- Eric Weisstein's World of Mathematics, Abundance.
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Select[Range[1, 10^6, 2], -10 <= DivisorSigma[1, #] - 2 # <= 10 &] (* Michael De Vlieger, Feb 22 2017 *)
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forstep(n=1,442365,2,if(abs(sigma(n)-2*n)<=10,print1(n,",")))
A088833
Numbers n whose abundance is 8: sigma(n) - 2n = 8.
Original entry on oeis.org
56, 368, 836, 11096, 17816, 45356, 77744, 91388, 128768, 254012, 388076, 2087936, 2291936, 13174976, 29465852, 35021696, 45335936, 120888092, 260378492, 381236216, 775397948, 3381872252, 4856970752, 6800228816, 8589344768, 44257207676, 114141404156
Offset: 1
Except first 4 terms of A045770 (1, 7, 10, and 49) are here: abundances = {-1,-6,-2,-41,8,8,8,8,8,8,8,8,8,8,8,8,8}.
A125246
Numbers m whose abundance sigma(m) - 2m = -4. Numbers whose deficiency is 4.
Original entry on oeis.org
5, 14, 44, 110, 152, 884, 2144, 8384, 18632, 116624, 8394752, 15370304, 73995392, 536920064, 2147581952, 34360131584, 27034175140420610, 36028797421617152, 576460753914036224
Offset: 1
The abundance of 5 = (1+5)-10 = -4.
More generally, whenever p = 2^k + 3 is prime (as p = 5 for k = 1), then A(2^(k-1)*p) = (2^k-1)*(p+1) - 2^k*p = 2^k - p - 1 = -4.
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[n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -4]; // Vincenzo Librandi, Sep 15 2016
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Select[Range[10^7], DivisorSigma[1, #] - 2 # == -4 &] (* Michael De Vlieger, Jul 18 2016 *)
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for(n=1,1000000,if(((sigma(n)-2*n)==-4),print1(n,",")))
A067702
Numbers k such that sigma(k) == 0 (mod k+2).
Original entry on oeis.org
12, 70, 88, 180, 1888, 4030, 5830, 32128, 521728, 1848964, 8378368, 34359083008, 66072609790, 549753192448, 259708613909470, 2251799645913088
Offset: 1
sigma(180) = 546 = 3(180+2), so 180 is in the sequence.
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Select[Range[84*10^5],Divisible[DivisorSigma[1,#],#+2]&] (* Harvey P. Dale, May 11 2018 *)
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isok(n) = sigma(n) % (n+2) == 0; \\ Michel Marcus, Nov 22 2013
A258885
Primitive weird numbers (A002975) having 6 distinct prime factors.
Original entry on oeis.org
1550860550, 44257207676, 66072609790
Offset: 1
a(1) = 1550860550 = 2 * 5^2 * 29 * 37 * 137 * 211 = A273815(1). (Abundance = 20)
a(2) = 44257207676 = 2^2 * 11 * 37 * 59 * 523 * 881. (Abundance = 8, cf. A088833)
a(3) = 66072609790 = 2 * 5 * 11 * 127^2 * 167 * 223 = A273815(3). (Abundance = 4, cf. A088832)
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(* copy the terms from A002975, assign them to 'lst' and then *)
Select[ lst, PrimeNu@# == 6 &]
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select(w->omega(w)==6, A002975) \\ Assuming that A002975 is defined as set or vector. - M. F. Hasler, Jul 12 2016
One more term added and definition corrected by
Giuseppe Melfi, Nov 02 2015
A045769
Numbers k such that sigma(k) == 4 (mod k).
Original entry on oeis.org
1, 3, 9, 12, 70, 88, 1888, 4030, 5830, 32128, 521728, 1848964, 8378368, 34359083008, 66072609790, 549753192448, 259708613909470, 2251799645913088, 9223372026117357568
Offset: 1
A275996
Numbers n whose abundance is 64: sigma(n) - 2n = 64.
Original entry on oeis.org
108, 220, 6808, 8968, 14008, 24448, 66928, 552568, 786208, 1020568, 5303488, 8229568, 10001848, 133685248, 499722448, 2608895488, 4733164768, 7163795488, 13707973408, 14468025568, 16122444736, 27339731968, 34351218688, 34672397728, 35371084288, 69657461248
Offset: 1
a(1) = 108, since sigma(108) - 2*108 = 280 - 216 = 64.
Cf.
A002025,
A063990,
A275997,
A088831,
A088832,
A088833,
A141547,
A175989,
A275701,
A066539,
A259180.
A156560
Primes of the form 2^n-5.
Original entry on oeis.org
3, 11, 59, 251, 1019, 4091, 262139, 1048571, 67108859, 4294967291, 68719476731, 72057594037927931, 73786976294838206459, 332306998946228968225951765070086139, 1361129467683753853853498429727072845819, 1427247692705959881058285969449495136382746619
Offset: 1
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[ a: n in [2..500] | IsPrime(a) where a is 2^n-5 ];
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Select[Table[2^n-5,{n,2,400}],PrimeQ] (* Vincenzo Librandi, Jul 26 2012 *)
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for(n=1,300,q=2^n-5;if(isprime(q),print(q))) /* gives more terms in <10secs */ \\ Joerg Arndt, Dec 03 2010
A181597
(N\{4})-perfect numbers, i.e., numbers m for which sigma(m)-4 = 2m, if 4|m, otherwise sigma(m) = 2m.
Original entry on oeis.org
6, 12, 88, 1888, 32128, 521728, 1848964, 8378368, 34359083008, 549753192448
Offset: 1
88 is in the sequence since sigma(88) = 180 and 180 - 4 = 2*88.
A275997
Numbers k whose deficiency is 64: 2k - sigma(k) = 64.
Original entry on oeis.org
134, 284, 410, 632, 1292, 1628, 4064, 9752, 12224, 22712, 66992, 72944, 403988, 556544, 2161664, 2330528, 8517632, 13228352, 14563832, 15422912, 20732792, 89472632, 134733824, 150511232, 283551872, 537903104, 731670272, 915473696, 1846850576, 2149548032, 2159587616
Offset: 1
a(1) = 134, since 2*134 - sigma(134) = 268 - 204 = 64.
Deficiency k:
A191363 (k=2),
A125246 (k=4),
A141548 (k=6),
A125247 (k=8),
A101223 (k=10),
A141549 (k=12),
A141550 (k=14),
A125248 (k=16),
A223608 (k=18),
A223607 (k=20),
A223606 (k=22),
A385255(k=24),
A275702 (k=26),
A387352 (k=32).
Abundance k:
A088831 (k=2),
A088832 (k=4),
A087167 (k=6),
A088833 (k=8),
A223609 (k=10),
A141545 (k=12),
A141546 (k=14),
A141547 (k=16),
A223610 (k=18),
A223611 (k=20),
A223612 (k=22),
A223613 (k=24),
A275701 (k=26),
A175989 (k=32),
A275996 (k=64),
A292626 (k=128).
Showing 1-10 of 16 results.
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