A218406 -id:A218406 - cp's OEIS frontend

A218407 Numbers k for which sigma(k)/k - 2/5 is an integer.

30, 140, 2480, 6200, 40640, 297600, 997920, 64995840, 167751680, 1502582400, 42949345280, 183196016640, 687193456640, 1447428787200, 63870637017600, 326676430080000, 20797363851264000, 24871926476966400, 42981218625945600, 404918548479244800

Offset: 1

Zdenek Cervenka, Oct 28 2012

nonn

a(12) > 10^11. - Donovan Johnson, Oct 31 2012
a(14) > 10^12. - Giovanni Resta, Nov 04 2012
Note that there are no terms here with abundancy 7/5 (k=1). - Michel Marcus, Jun 26 2013

Cf. A218406, A218408, A218427.

a(8)-a(11) from Donovan Johnson, Oct 31 2012
a(12)-a(13) from Giovanni Resta, Nov 04 2012
More terms from Michel Marcus, Jun 26 2013

A218408 Numbers k for which sigma(k)/k - 3/5 is an integer.

Original entry on oeis.org

15, 90, 3360, 2618880, 5059200, 4873497600, 7381524480, 27990144000, 57846297600, 4609292688000, 4440104532864000, 106644933787392000, 164741543366400000, 454310107592140800, 1084892424295680000, 1160492902900531200, 10932800808939609600

Offset: 1

Zdenek Cervenka, Oct 28 2012

nonn

a(10) > 10^11. - Donovan Johnson, Oct 31 2012

a(10) > 10^12. - Giovanni Resta, Nov 04 2012

Cf. A218406, A218407, A218427.

a(6)-a(9) from Donovan Johnson, Oct 31 2012

More terms from Michel Marcus, Jun 26 2013

A218427 Numbers k for which sigma(k)/k - 4/5 is an integer.

Original entry on oeis.org

10, 60, 1170, 114660, 72602880, 668304000, 714954240, 1307124000, 1381161600, 2701389600, 8052817920, 10181689600, 643773312000, 1330464844800, 2015156183040, 3522876144480, 15462510336000, 23885971200000, 702577007193600, 908714417345280

Offset: 1

Zdenek Cervenka, Oct 28 2012

nonn

a(13) > 10^11. - Donovan Johnson, Oct 31 2012

a(14) > 10^12. - Giovanni Resta, Nov 04 2012

M. Drennen, T. Gunter, P. Johnson and J. Ward, The Loneliest Number
Jeffrey Ward, Does Ten Have a Friend?, arXiv:0806.1001 [math.NT], 2008.

Cf. A218406, A218407, A218408.

a(5)-a(12) from Donovan Johnson, Oct 31 2012
a(13) from Giovanni Resta, Nov 04 2012
More terms from Michel Marcus, Jun 26 2013

A326200 Lexicographically earliest sequence such that a(i) = a(j) => sigma(i)/i = sigma(j)/j for all i, j.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 6, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90

Offset: 1

Antti Karttunen, Jun 13 2019

nonn

Restricted growth sequence transform of the abundancy index of n.
For all i, j:
  a(i) = a(j) <=> A094759(i) = A094759(j),
  a(i) = a(j) => A017665(i) = A017665(j),
  a(i) = a(j) => A017666(i) = A017666(j).

Antti Karttunen, Table of n, a(n) for n = 1..105664
Achim Flammenkamp, The Multiply Perfect Numbers Page

Cf. A000396 (positions of 6's), A005820 (positions of 119's).
Cf. A017665, A017666, A074902, A094759.
Cf. A218406, A218407, A218408, A218427, A326202.

up_to = 105664; \\ (In the same equivalence class as 78, 364 and 6448).
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
v326200 = rgs_transform(vector(up_to,n,sigma(n)/n));
A326200(n) = v326200[n];

A364976 3-abundant numbers k such that k/(sigma(k)-3*k) is an integer.

Original entry on oeis.org

180, 240, 360, 420, 540, 600, 780, 1080, 1344, 1872, 1890, 2016, 2184, 2352, 2376, 2688, 3192, 3276, 3744, 4284, 4320, 4680, 5292, 5376, 5796, 6048, 6552, 7128, 7440, 8190, 10416, 13776, 14850, 18600, 19824, 19872, 20496, 21528, 22932, 25056, 26208, 26496, 26784

Offset: 1

Amiram Eldar, Aug 15 2023

nonn

Analogous to A153501 as 3-abundant numbers (A068403) are analogous to abundant numbers (A005101).

Numbers k such that the sum of the divisors of k except for one of them is equal to 3*k.

			180 is a term since sigma(180) - 3*180 = 6 > 0 and 180 is divisible by 6.

Amiram Eldar, Table of n, a(n) for n = 1..576 (terms below 2.5*10^10)

Subsequence of A068403.
A027687 is a subsequence.
Cf. A000203 (sigma), A005101, A005820, A055153, A153501, A160320, A218404, A218406, A329189, A364977.

Select[Range[27000], (d = DivisorSigma[1, #] - 3*#) > 0 && Divisible[#, d] &]

is(n) = {my(d = sigma(n) - 3*n); d > 0 && n%d == 0;}

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A218407 Numbers k for which sigma(k)/k - 2/5 is an integer.

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A218408 Numbers k for which sigma(k)/k - 3/5 is an integer.

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A218427 Numbers k for which sigma(k)/k - 4/5 is an integer.

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A326200 Lexicographically earliest sequence such that a(i) = a(j) => sigma(i)/i = sigma(j)/j for all i, j.

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A364976 3-abundant numbers k such that k/(sigma(k)-3*k) is an integer.

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Mathematica

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