A218409 -id:A218409 - cp's OEIS frontend

A218410 Numbers k for which sigma(k)/k - 3/7 is an integer.

840, 55860, 1089270, 3666432, 5322240, 8714160, 10281600, 20109600, 21785400, 32104800, 9904204800, 10334134272, 4660073935104, 7322605472000, 11887123248000, 15387946358400, 78599399424000, 516876560449536, 750304684523520, 812193794048000

Offset: 1

Zdenek Cervenka, Oct 28 2012

nonn

a(13) > 10^11. - Donovan Johnson, Oct 31 2012
a(13) > 10^12. - Giovanni Resta, Nov 04 2012
Note that there are no terms with abundancy 10/7 or 17/7. - Michel Marcus, Jun 25 2013

Cf. A218428, A218409, A218411, A218412, A218413.

a(5)-a(12) from Donovan Johnson, Oct 31 2012

More terms from Michel Marcus, Jun 25 2013

A218411 Numbers k for which sigma(k)/k - 4/7 is an integer.

Original entry on oeis.org

280, 18620, 411264, 804384, 871416, 1222144, 1284192, 164989440, 270138960, 318729600, 326781000, 396168192, 481572000, 623397600, 675347400, 995248800, 3444711424, 4426793280, 307030348800, 465036042240, 880719036120

Offset: 1

Zdenek Cervenka, Oct 28 2012

nonn

a(19) > 10^11. - Donovan Johnson, Oct 31 2012

a(22) > 10^12. - Giovanni Resta, Nov 04 2012

Cf. A218428, A218409, A218410, A218412, A218413.

a(8)-a(18) from Donovan Johnson, Oct 31 2012

a(19)-a(21) from Giovanni Resta, Nov 04 2012

A218412 Numbers k for which sigma(k)/k - 5/7 is an integer.

Original entry on oeis.org

14, 588, 2520, 11466, 167580, 10999296, 67858560, 132723360, 8644446720, 31002402816, 65367751680, 10941315840000, 13980221805312, 24365070213120, 225855341712000, 317483934427296, 901703887257600, 1550629681348608, 8494794723340800

Offset: 1

Zdenek Cervenka, Oct 28 2012

nonn

a(12) > 10^11. - Donovan Johnson, Oct 31 2012

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

Cf. A218428, A218409, A218410, A218411, A218413.

a(6)-a(11) from Donovan Johnson, Oct 31 2012

More terms from Michel Marcus, Jun 25 2013

A218413 Numbers k for which sigma(k)/k - 6/7 is an integer.

Original entry on oeis.org

168, 11172, 217854, 228480, 446880, 220093440, 5228496000, 10805558400, 14091504577920, 583455456460800, 2583890834482298880, 5510058011880428160, 224050000769667072000, 1022756201136515973120, 1314073124731389718080, 2661277331943365990400

Offset: 1

Zdenek Cervenka, Oct 28 2012

nonn

a(9) > 10^11. - Donovan Johnson, Oct 31 2012
a(9) > 10^12. - Giovanni Resta, Nov 04 2012
Note that there are no terms with abundancy 13/7. - Michel Marcus, Jun 25 2013

Cf. A218428, A218409, A218410, A218411, A218412.

a(6)-a(8) from Donovan Johnson, Oct 31 2012

More terms from Michel Marcus, Jun 25 2013

A218428 Numbers k for which sigma(k)/k - 1/7 is an integer.

Original entry on oeis.org

7, 56, 3724, 333312, 939466752, 88884432000, 95088913920, 183694492800, 85621850496000, 120354474240000, 176951824358400, 239555577824640, 268015772344320, 2056513874688000, 9918742759833600, 93442741956748800, 149180517860774400, 230762478968017920

Offset: 1

Zdenek Cervenka, Oct 28 2012

nonn

a(8) > 10^11. - Donovan Johnson, Oct 31 2012
a(9) > 10^12. - Giovanni Resta, Nov 04 2012
Note that there are no terms here with abundancy 29/7. - Michel Marcus, Jun 25 2013

Cf. A218409, A218410, A218411, A218412, A218413.

a(5)-a(7) from Donovan Johnson, Oct 31 2012
a(8) from Giovanni Resta, Nov 04 2012
More terms from Michel Marcus, Jun 25 2013

A347169 Numbers k for which sigma(k)/k = 16/7.

Original entry on oeis.org

42, 3472, 56896, 544635, 234852352, 60129083392, 962070839296, 16140901056979664896, 18609191940988822212582848311676895232

Offset: 1

Timothy L. Tiffin, Aug 20 2021

This sequence will contain terms of the form 7*P, where P is a perfect number (A000396) not divisible by 7. Proof: sigma(7*P)/(7*P) = sigma(7)*sigma(P)/(7*P) = 8*(2*P)/(7*P) = 16/7. QED

Terms ending in "2" or "96" have this form. Example: a(n) = 7*A000396(n) for n = 1, 5, 6, 7, 8, 9 and a(n) = 7*A000396(n+1) for n = 2, 3.

			544635 is a term, since sigma(544635)/544635 = 1244880/544635 = 16/7.

G. P. Michon, Multiperfect Numbers and Hemiperfect Numbers
Walter Nissen, Abundancy: Some Resources (preliminary version 4)
Walter Nissen, Primitive Friendly Pairs with friends < 2^34 with denom < 20000

Cf. A000203, A000396.

Subsequence of A005101 and A218409.

Select[Range[5*10^8], DivisorSigma[1, #]/# == 16/7 &]
Do[If[DivisorSigma[1, k]/k == 16/7, Print[k]], {k, 5*10^8}]

a(8)-a(9) from Michel Marcus, Aug 21 2021

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A218410 Numbers k for which sigma(k)/k - 3/7 is an integer.

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A218411 Numbers k for which sigma(k)/k - 4/7 is an integer.

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A218412 Numbers k for which sigma(k)/k - 5/7 is an integer.

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A218413 Numbers k for which sigma(k)/k - 6/7 is an integer.

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A218428 Numbers k for which sigma(k)/k - 1/7 is an integer.

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A347169 Numbers k for which sigma(k)/k = 16/7.

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