A055713 -id:A055713 - 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

A055712 Numbers k such that k | sigma_8(k).

Original entry on oeis.org

1, 84, 156, 204, 364, 476, 514, 1092, 1428, 2316, 2652, 2892, 6069, 6188, 6748, 12138, 12532, 16212, 16388, 18564, 20244, 24276, 30108, 37596, 39372, 49164, 63291, 78897, 87724, 99202, 114716, 126582, 147679, 157794, 167331

Offset: 1

Robert G. Wilson v, Jun 09 2000

nonn

sigma_8(k) is the sum of the 8th powers of the divisors of k (A013956).

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

Amiram Eldar, Table of n, a(n) for n = 1..1000
Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

Cf. A013956.

Cf. A055709, A055710, A055711, A055713.

Do[If[Mod[DivisorSigma[8, n], n]==0, Print[n]], {n, 1, 10000}]
Select[Range[170000],Divisible[DivisorSigma[8,#],#]&] (* Harvey P. Dale, Sep 15 2019 *)

is(n)=sigma(n,8)%n==0 \\ Charles R Greathouse IV, Feb 04 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

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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A055712 Numbers k such that k | sigma_8(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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A055715 Numbers k such that k | sigma_11(k).

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