A019283 -id:A019283 - cp's OEIS frontend

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.

24, 1536, 47360, 343976, 572941926400

Offset: 1

See also the Cohen-te Riele links under A019276.
No other terms < 5*10^11. - Jud McCranie, Feb 08 2012
572941926400 is also a term. See comment in A019278. - Michel Marcus, May 15 2016
a(6) > 4*10^12, if it exists. - Giovanni Resta, Feb 26 2020

Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

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

a(5) from Giovanni Resta, Feb 26 2020

A019281 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 (2,3)-perfect numbers.

Original entry on oeis.org

8, 21, 512

Offset: 1

N. J. A. Sloane

See also the Cohen-te Riele links under A019276.
No further term < 10^9 [see Table 1].
No other terms < 5*10^11. - Jud McCranie, Feb 08 2012
a(4) > 4*10^12, if it exists. - Giovanni Resta, Feb 26 2020

Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.
Experimental Mathematics, Home Page.

Cf. A019278, A019279, A019282, A019283, A019284, A019285, A019286, A019287, A019288, A019289, A019290, A019291.

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

N. J. A. Sloane

See also the Cohen-te Riele links under A019276.
No other terms < 5*10^11. - Jud McCranie, Feb 08 2012
a(5) > 4*10^12, if it exists. - Giovanni Resta, Feb 26 2020

Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

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

a(4) from Jud McCranie, Feb 08 2012

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

N. J. A. Sloane

If 2^p-1 is a Mersenne prime greater than 3 then m = 15*2^(p-1) is in the sequence. Because sigma(sigma(m)) = sigma(15*2^(p-1)) = sigma(24*(2^p-1)) = 60*2^p = 8*(15*2^(p-1)) = 8*m. So for n>1 15/2*(A000668(n)+1) is in the sequence. 60, 240, 960, 61440, 983040, 3932160, 16106127360 and 1729382256910270464042 are such terms. - Farideh Firoozbakht, Dec 05 2005
See also the Cohen-te Riele links under A019276.
No other terms < 5*10^11. - Jud McCranie, Feb 08 2012
1422976331052 is also a term. See comment in A019278. - Michel Marcus, May 15 2016
a(25) > 4*10^12. - Giovanni Resta, Feb 26 2020

G. L. Cohen and H. J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

Cf. A000668, A019276, A019278, A019279, A019281, A019282, A019283, A019284, A019285, A019286, A019287, A019288, A019289, A019290, A019291.

isok(n) = sigma(sigma(n))/n == 8; \\ Michel Marcus, May 15 2016

a(19) from Jud McCranie, Nov 13 2001
a(20)-a(21) from Jud McCranie, Jan 29 2012
a(22)-a(24) from Giovanni Resta, Feb 26 2020

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

N. J. A. Sloane

See also the Cohen-te Riele links under A019276.
No other terms < 5*10^11. - Jud McCranie, Feb 08 2012
4010593484800 is also a term. See comment in A019278. - Michel Marcus, May 15 2016

Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

Cf. A000668, A019278, A019279, A019281, A019282, A019283, A019284, A019285, A019286, A019287, A019288, A019289, A019290, A019291.

isok(n) = sigma(sigma(n))/n  == 9; \\ Michel Marcus, May 12 2016

a(8) by Jud McCranie, Jan 28 2012

a(9) from Giovanni Resta, Feb 26 2020

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

N. J. A. Sloane

See also the Cohen-te Riele links under A019276.
No other terms < 5*10^11. - Jud McCranie, Feb 08 2012
a(11) > 4*10^12, if it exists. - Giovanni Resta, Feb 26 2020

G. L. Cohen and H. J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

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

N. J. A. Sloane

See also the Cohen-te Riele links under A019276.
No other terms < 5*10^11. - Jud McCranie, Feb 08 2012
a(4) > 4*10^12. - Giovanni Resta, Feb 26 2020
53283599155200, 2914255525994496 and 3887055949004800 are also terms. - Michel Marcus, Feb 27 2020

Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

Cf. A019278, A019279, A019281, A019282, A019283, A019284, A019285, A019286, A019287, A019289, A019290, A019291.

isok(n) = sigma(sigma(n))/n  == 11; \\ Michel Marcus, Feb 27 2020

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

N. J. A. Sloane

See also the Cohen-te Riele links under A019276.
No others < 5*10^11. - Jud McCranie, Feb 08 2012
a(14) > 4*10^12. - Giovanni Resta, Feb 26 2020
6640556211576, 82863343951872, 182140970374656, 480965999895576, 590660008673280, 886341160140800, 5562693163417600, 9386507580211200 are also terms. - Michel Marcus, Feb 27 2020

Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

Cf. A019278, A019279, A019281, A019282, A019283, A019284, A019285, A019286, A019287, A019288, A019290, A019291.

isok(n) = sigma(sigma(n))/n  == 12; \\ Michel Marcus, Feb 27 2020

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

N. J. A. Sloane

See also the Cohen-te Riele links under A019276.
No other terms < 5*10^11. - Jud McCranie, Feb 08 2012
11383810648416 is also a term. See comment in A019278. - Michel Marcus, May 15 2016
a(5) > 4*10^12. - Giovanni Resta, Feb 26 2020
50248050278400, 117245450649600, 86575337046016000 are also terms. - Michel Marcus, Feb 27 2020

Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

Cf. A019276, A019278, A019279, A019281, A019282, A019283, A019284, A019285, A019286, A019287, A019288, A019289, A019291.

isok(n) = sigma(sigma(n))/n == 13; \\ Michel Marcus, May 15 2016

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

N. J. A. Sloane

nonn

See also the Cohen-te Riele links under A019276.
No other terms < 5*10^11. - Jud McCranie, Feb 08 2012
36095341363200 is also a term. See comment in A019278. - Michel Marcus, May 15 2016
a(11) > 4*10^12. - Giovanni Resta, Feb 26 2020

Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

Cf. A019276, A019278, A019279, A019281, A019282, A019283, A019284, A019285, A019286, A019287, A019288, A019289, A019290.

isok(n) = sigma(sigma(n))/n == 14; \\ Michel Marcus, May 15 2016

More terms from Jud McCranie, Nov 13 2001
a(9) from Jud McCranie, Jan 28 2012
a(10) from Giovanni Resta, Feb 26 2020

cp's OEIS Frontend

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.

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A019281 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 (2,3)-perfect numbers.

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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.

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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.

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PARI

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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.

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Programs

PARI

Extensions

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.

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Author

Keywords

Comments

Links

Crossrefs

Extensions

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.

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Author

Keywords

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Crossrefs

Programs

PARI

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.

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Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Extensions

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.

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