A328063
Amicable pairs with the property that the number of divisors of the smaller member is greater than the number of divisors of the larger member.
Original entry on oeis.org
220, 284, 6232, 6368, 12285, 14595, 17296, 18416, 63020, 76084, 69615, 87633, 79750, 88730, 100485, 124155, 122265, 139815, 141664, 153176, 142310, 168730, 185368, 203432, 280540, 365084, 308620, 389924, 319550, 430402, 356408, 399592, 600392, 669688, 609928, 686072, 624184, 691256
Offset: 1
Consider the amicable pair [220, 284]. The smaller member has 12 divisors, they are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220. The larger member has 6 divisors, they are 1, 2, 4, 71, 142, 284. The number of divisors of 220 is greater than the number of divisors of 284, so the amicable pair [220, 284] is in the sequence.
-
seq = {}; s[n_] := DivisorSigma[1, n] - n; Do[m = s[n]; If[m > n && s[m] == n && DivisorSigma[0, n] > DivisorSigma[0, m], seq = Join[seq, {n, m}]], {n, 1, 7*10^5}]; seq (* Amiram Eldar, Oct 11 2019 *)
A328064
Amicable pairs with the property that both members have the same number of divisors.
Original entry on oeis.org
1184, 1210, 2620, 2924, 5020, 5564, 10744, 10856, 66928, 66992, 67095, 71145, 122368, 123152, 171856, 176336, 176272, 180848, 196724, 202444, 437456, 455344, 503056, 514736, 522405, 525915, 1077890, 1099390, 1154450, 1189150, 1280565, 1340235, 1358595, 1486845, 1392368, 1464592, 2082464, 2090656
Offset: 1
Consider the amicable pair [1184, 1210]. The smaller member has 12 divisors, they are 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592, 1184. The larger member has 12 divisors, they are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210. The number of divisors of 1184 is equal to the number of divisors of 1210, so the amicable pair [1184, 1210] is in the sequence.
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seq = {}; s[n_] := DivisorSigma[1, n] - n; Do[m = s[n]; If[m > n && s[m] == n && DivisorSigma[0, n] == DivisorSigma[0, m], seq = Join[seq, {n, m}]], {n, 1, 10^6}]; seq (* Amiram Eldar, Oct 11 2019 *)
A328065
Amicable pairs with the property that the number of divisors of the smaller member is twice the number of divisors of the larger member.
Original entry on oeis.org
220, 284, 12285, 14595, 17296, 18416, 63020, 76084, 69615, 87633, 79750, 88730, 100485, 124155, 122265, 139815, 142310, 168730, 185368, 203432, 308620, 389924, 356408, 399592, 600392, 669688, 609928, 686072, 624184, 691256, 635624, 712216, 643336, 652664, 667964, 783556, 726104, 796696, 898216, 980984
Offset: 1
Consider the amicable pair [220, 284]. The smaller member has 12 divisors, they are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220. The larger member has 6 divisors, they are 1, 2, 4, 71, 142, 284. The number of divisors of 220 is twice the number of divisors of 284, so the amicable pair [220, 284] is in the sequence.
-
seq = {}; s[n_] := DivisorSigma[1, n] - n; Do[m = s[n]; If[m > n && s[m] == n && DivisorSigma[0, n] == 2 * DivisorSigma[0, m], seq = Join[seq, {n, m}]], {n, 1, 10^6}]; seq (* Amiram Eldar, Oct 11 2019 *)
A339682
Lesser of amicable pair a < b such that the ratio of their number of divisors d(b)/d(a) sets a new record.
Original entry on oeis.org
220, 1184, 469028, 11693290, 37784810, 6057622044705, 14772536572365, 35019687151575, 19245649704560895, 42564348058073842, 1004007953218033575, 6778057036176125612
Offset: 1
The least pair of amicable numbers, (220, 284), has a ratio of the numbers of divisors d(284)/d(220) = 6/12 = 1/2.
The next pair with a larger ratio is (1184, 1210) whose ratio is d(1210)/d(1184) = 12/12 = 1.
-
s[n_] := DivisorSigma[1, n] - n; rm = 0; seq = {}; Do[m = s[n]; If[m > n && s[m] == n && (r = Divide @@ DivisorSigma[0, {m, n}]) > rm, rm = r; AppendTo[seq, n]], {n, 1, 10^7}]; seq
A339683
Larger of amicable pair a < b such that the ratio of their number of divisors d(b)/d(a) sets a new record.
Original entry on oeis.org
284, 1210, 486178, 12361622, 39944086, 6119799324639, 15309719733555, 36680009488425, 20386078790473473, 43160565196326158, 1052608596326926425, 6924667299336450388
Offset: 1
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s[n_] := DivisorSigma[1, n] - n; rm = 0; seq = {}; Do[m = s[n]; If[m > n && s[m] == n && (r = Divide @@ DivisorSigma[0, {m, n}]) > rm, rm = r; AppendTo[seq, m]], {n, 1, 10^7}]; seq
Showing 1-5 of 5 results.
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