A055712 -id:A055712 - cp's OEIS frontend

A055709 Numbers k such that k | sigma_5(k).

1, 6, 22, 28, 66, 120, 198, 264, 308, 366, 440, 604, 672, 924, 984, 1320, 1464, 1694, 1717, 2013, 2296, 2464, 2574, 2970, 3434, 3608, 3960, 4026, 4228, 4598, 4920, 5082, 5151, 5348, 6200, 6600, 6644, 6776, 6868, 6888, 7320, 7392, 8052, 8128, 9504

Offset: 1

Robert G. Wilson v, Jun 09 2000

nonn

sigma_5(k) is the sum of the 5th powers of the divisors of k (A001160).

Problem 11090 proves that this sequence is infinite. - T. D. Noe, Apr 18 2006

Charles R Greathouse IV, Table of n, a(n) for n = 1..7000
Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

Cf. A001160.

Cf. A055710, A055711, A055712, A055713.

Do[If[Mod[DivisorSigma[5, n], n]==0, Print[n]], {n, 1, 15000}]
Select[Range[10000],Divisible[DivisorSigma[5,#],#]&] (* Harvey P. Dale, Aug 09 2013 *)

is(n)=sigma(n,5)%n==0 \\ Charles R Greathouse IV, Feb 01 2013

A055710 Numbers k such that k | sigma_6(k).

Original entry on oeis.org

1, 10, 26, 60, 65, 130, 150, 228, 260, 442, 650, 780, 876, 988, 1105, 1140, 1460, 1690, 1950, 2210, 2850, 2964, 3211, 3796, 4380, 4420, 4940, 5070, 5475, 5548, 6010, 6422, 8840, 9633, 10950, 11050, 11388, 11972, 12350, 12818, 13260, 13756, 14820, 16644

Offset: 1

Robert G. Wilson v, Jun 09 2000

nonn

sigma_6(k) is the sum of the 6th powers of the divisors of k (A013954).

Problem 11090 proves that this sequence is infinite. - T. D. Noe, Apr 18 2006

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..450 from Harvey P. Dale)
Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

Cf. A013954.

Cf. A055709, A055711, A055712, A055713.

Do[If[Mod[DivisorSigma[6, n], n]==0, Print[n]], {n, 1, 25000}]
Select[Range[20000],Divisible[DivisorSigma[6,#],#]&] (* Harvey P. Dale, Jun 04 2015 *)

is(n)=sigma(n,6)%n==0 \\ Charles R Greathouse IV, Feb 04 2013

A055711 Numbers k such that k | sigma_7(k).

Original entry on oeis.org

1, 6, 28, 86, 120, 145, 258, 290, 435, 496, 580, 588, 672, 696, 870, 946, 1032, 1305, 1720, 1740, 2245, 2610, 2712, 2838, 3164, 3282, 3408, 3480, 3724, 3784, 4060, 4490, 5160, 5220, 6735, 6786, 6960, 7830, 8514, 8980, 9436, 9492, 9632, 9976

Offset: 1

Robert G. Wilson v, Jun 09 2000

nonn

sigma_7(k) is the sum of the 7th powers of the divisors of k (A013955).

Problem 11090 proves that this sequence is infinite. - T. D. Noe, Apr 18 2006

Amiram Eldar, Table of n, a(n) for n = 1..10000
Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

Cf. A013955.

Cf. A055709, A055710, A055712, A055713.

Do[If[Mod[DivisorSigma[7, n], n]==0, Print[n]], {n, 1, 10000}]

is(n)=sigma(n,7)%n==0 \\ Charles R Greathouse IV, Feb 04 2013

A055713 Numbers k such that k | sigma_9(k).

Original entry on oeis.org

1, 6, 38, 42, 54, 114, 120, 135, 168, 190, 216, 222, 266, 270, 280, 285, 312, 342, 378, 456, 496, 540, 570, 672, 728, 760, 798, 840, 888, 945, 1026, 1064, 1080, 1140, 1330, 1512, 1554, 1560, 1710, 1782, 1806, 1862, 1890, 1962, 1976, 1995, 1998, 2160, 2166

Offset: 1

Robert G. Wilson v, Jun 09 2000

nonn

sigma_9(k) is the sum of the 9th powers of the divisors of k (A013957).

Problem 11090 proves that this sequence is infinite. - T. D. Noe, Apr 18 2006

Amiram Eldar, Table of n, a(n) for n = 1..10000
Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

Cf. A013957.

Cf. A055709, A055710, A055711, A055712.

Do[If[Mod[DivisorSigma[9, n], n]==0, Print[n]], {n, 1, 5000}]

is(n)=sigma(n,9)%n==0 \\ Charles R Greathouse IV, Feb 04 2013

A066284 a(n) = A066135(4*n).

Original entry on oeis.org

34, 84, 34, 84, 34, 194, 34, 84, 34, 84, 34, 228, 34, 84, 34, 84, 34, 194, 34, 84, 34, 84, 34, 228, 34, 84, 34, 84, 34, 194, 34, 84, 34, 84, 34, 386, 34, 84, 34, 84, 34, 194, 34, 84, 34, 84, 34, 228, 34, 84, 34, 84, 34, 194, 34, 84, 34, 84, 34, 228, 34, 84, 34, 84, 34, 194

Offset: 1

Labos Elemer, Dec 11 2001

nonn

a(n) <= 2p, where p = A002586(4n) is the least prime factor of (1 + 16^n). (See the Comment in A066135.) - Jonathan Sondow, Nov 23 2012

			First 3 terms correspond to entries of other sequences as follows: a(1)=A046763(2), a(2)=A055712(2), a(3)=A055716(2).
From _Michael De Vlieger_, Jul 17 2017: (Start)
First position of values, with observations pertaining to values for 1 <= n <= 3000:
    Value   Position   Observations:
    --------------------------------
       34     1        All odd.
       84     2        In A047235.
      194     6        In A017593.
      228    12
      386    36
     1282    72
     1538   144
     3084   288
   147468   576
     1956   864
  1046532  1152
    24578  2304
     3252  2880
(End)

Michael De Vlieger, Table of n, a(n) for n = 1..1000

Cf. A066135, A046761, A046762, A046763, A055709-A055717, A007691, A001159.

Table[m = 2; While[Mod[DivisorSigma[4 n, m], m] > 0, m++]; m, {n, 66}] (* Michael De Vlieger, Jul 17 2017 *)

a(n) = {n *= 4; my(m = 2); while (sigma(m, n) % m, m++); m;} \\ Michel Marcus, Oct 02 2016

a(n) = Min{x : sigma_4n(x) mod x = 0, x > 1}

A055715 Numbers k such that k | sigma_11(k).

Original entry on oeis.org

1, 6, 28, 120, 402, 496, 644, 672, 920, 1366, 1608, 1932, 2680, 2760, 3417, 3966, 4098, 4623, 4975, 5152, 6210, 6834, 8040, 8128, 8280, 9246, 9528, 9950, 12294, 13668, 15008, 15456, 15864, 16392, 18492, 19900, 24120, 24840, 25954, 27320, 27336, 29850, 30240, 32760

Offset: 1

Robert G. Wilson v, Jun 09 2000

nonn

sigma_11(k) is the sum of the 11th powers of the divisors of k (A013959).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A013959.

Cf. A007691, A046762, A046763, A046764, A055709, A055710, A055711, A055712, A055713, A055714.

Do[If[Mod[DivisorSigma[11, n], n]==0, Print[n]], {n, 1, 40000}]

isok(k) = (sigma(k, 11) % k) == 0; \\ Michel Marcus, Nov 09 2019

a(37)-a(40) corrected and more terms added by Amiram Eldar, Nov 09 2019

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A055709 Numbers k such that k | sigma_5(k).

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A055710 Numbers k such that k | sigma_6(k).

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A055711 Numbers k such that k | sigma_7(k).

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A055713 Numbers k such that k | sigma_9(k).

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A066284 a(n) = A066135(4*n).

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A055715 Numbers k such that k | sigma_11(k).

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