A019284
Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,7)-perfect numbers.
Original entry on oeis.org
24, 1536, 47360, 343976, 572941926400
Offset: 1
Cf.
A000668,
A019278,
A019279,
A019281,
A019282,
A019283,
A019285,
A019286,
A019287,
A019288,
A019289,
A019290,
A019291.
-
Select[Range[50000], DivisorSigma[1, DivisorSigma[1, #]]/# == 7 &] (* Robert Price, Apr 07 2019 *)
-
isok(n) = sigma(sigma(n))/n == 7; \\ Michel Marcus, May 12 2016
A019282
Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,4)-perfect numbers.
Original entry on oeis.org
15, 1023, 29127, 355744082763
Offset: 1
Cf.
A019278,
A019279,
A019281,
A019283,
A019284,
A019285,
A019286,
A019287,
A019288,
A019289,
A019290,
A019291.
-
Select[Range[100000], DivisorSigma[1, DivisorSigma[1, #]]/# == 4 &] (* Robert Price, Apr 07 2019 *)
-
isok(n) = sigma(sigma(n))/n == 4; \\ Michel Marcus, May 12 2016
A019285
Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,8)-perfect numbers.
Original entry on oeis.org
60, 240, 960, 4092, 16368, 58254, 61440, 65472, 116508, 466032, 710400, 983040, 1864128, 3932160, 4190208, 67043328, 119304192, 268173312, 1908867072, 7635468288, 16106127360, 711488165526, 1098437885952, 1422976331052
Offset: 1
Cf.
A000668,
A019276,
A019278,
A019279,
A019281,
A019282,
A019283,
A019284,
A019285,
A019286,
A019287,
A019288,
A019289,
A019290,
A019291.
A019286
Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,9)-perfect numbers.
Original entry on oeis.org
168, 10752, 331520, 691200, 1556480, 1612800, 106151936, 5099962368, 4010593484800
Offset: 1
Cf.
A000668,
A019278,
A019279,
A019281,
A019282,
A019283,
A019284,
A019285,
A019286,
A019287,
A019288,
A019289,
A019290,
A019291.
A019287
Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,10)-perfect numbers.
Original entry on oeis.org
480, 504, 13824, 32256, 32736, 1980342, 1396617984, 3258775296, 14763499520, 38385098752
Offset: 1
Cf.
A019278,
A019279,
A019281,
A019282,
A019283,
A019284,
A019285,
A019286,
A019288,
A019289,
A019290,
A019291.
More terms from
Jud McCranie, Nov 13 2001; a(9) Jan 29 2012, a(10) Feb 08 2012
A019288
Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,11)-perfect numbers.
Original entry on oeis.org
4404480, 57669920, 238608384
Offset: 1
Cf.
A019278,
A019279,
A019281,
A019282,
A019283,
A019284,
A019285,
A019286,
A019287,
A019289,
A019290,
A019291.
A019289
Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,12)-perfect numbers.
Original entry on oeis.org
2200380, 8801520, 14913024, 35206080, 140896000, 459818240, 775898880, 2253189120, 16785793024, 22648550400, 36051025920, 51001180160, 144204103680
Offset: 1
Cf.
A019278,
A019279,
A019281,
A019282,
A019283,
A019284,
A019285,
A019286,
A019287,
A019288,
A019290,
A019291.
More terms from
Jud McCranie, Nov 13 2001, a(9) Feb 01 2012, a(10)-a(13) on Feb 08 2012
A019290
Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,13)-perfect numbers.
Original entry on oeis.org
57120, 932064, 3932040, 251650560
Offset: 1
Cf.
A019276,
A019278,
A019279,
A019281,
A019282,
A019283,
A019284,
A019285,
A019286,
A019287,
A019288,
A019289,
A019291.
A019291
Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,14)-perfect numbers.
Original entry on oeis.org
217728, 1278720, 2983680, 5621760, 14008320, 298721280, 955367424, 1874780160, 4874428416, 1957928934528
Offset: 1
Cf.
A019276,
A019278,
A019279,
A019281,
A019282,
A019283,
A019284,
A019285,
A019286,
A019287,
A019288,
A019289,
A019290.
A192293
Let sigma*_m (n) be the result of applying the sum of anti-divisors m times to n; call n (m,k)-anti-perfect if sigma*_m (n) = k*n; this sequence gives the (2,3)-anti-perfect numbers.
Original entry on oeis.org
32, 98, 2524, 199282, 1336968
Offset: 1
sigma*(32)= 3+5+7+9+13+21=58; sigma*(58)= 3+4+5+9+13+23+39=96 and 3*32=96.
sigma*(98)= 3+4+5+13+15+28+39+65=172; sigma*(172)= 3+5+7+8+15+23+49+69+115=294 and 3*98=294.
sigma*(2524)= 3+7+8+9+11+17+27+33+49+51+99+103+153+187+297+459+561+721+1683=4478; sigma*(4478)= 3+4+5+9+13+15+45+53+169+199+597+689+995+1791+2985=7572 and 3*2524=7572.
-
with(numtheory): P:= proc(n) local i,j,k,s,s1; for i from 3 to n do
k:=0; j:=i; while j mod 2 <> 1 do k:=k+1; j:=j/2; od; s:=sigma(2*i+1)+sigma(2*i-1)+sigma(i/2^k)*2^(k+1)-6*i-2;
k:=0; j:=s; while j mod 2 <> 1 do k:=k+1; j:=j/2; od; s1:=sigma(2*s+1)+sigma(2*s-1)+sigma(s/2^k)*2^(k+1)-6*s-2;
if s1/i=3 then print(i); fi; od; end: P(10^9);
-
from sympy import divisors
def antidivisors(n):
return [2*d for d in divisors(n) if n > 2*d and n % (2*d)] + \
[d for d in divisors(2*n-1) if n > d >=2 and n % d] + \
[d for d in divisors(2*n+1) if n > d >=2 and n % d]
A192293_list = []
for n in range(1,10**4):
if 3*n == sum(antidivisors(sum(antidivisors(n)))):
A192293_list.append(n) # Chai Wah Wu, Dec 02 2014
Showing 1-10 of 11 results.
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