A324709
Larger of tri-unitary amicable numbers pair: numbers (m, n) such that tsigma(m) = tsigma(n) = m + n, where tsigma(n) is the sum of the tri-unitary divisors of n (A324706).
Original entry on oeis.org
126, 846, 1260, 8460, 11760, 10856, 14595, 17700, 49308, 83142, 62700, 71145, 73962, 83904, 107550, 88730, 131100, 168730, 149952, 196650, 203432, 306612, 365700, 399592, 419256, 548550, 721962, 669688, 831420, 686072, 691256, 712216, 652664, 661824, 827700
Offset: 1
126 is in the sequence since it is the larger of the amicable pair (114, 126): tsigma(114) = tsigma(126) = 114 + 126.
-
f[p_, e_] := If[e == 3, (p^4-1)/(p-1), If[e==6, (p^8-1)/(p^2-1), p^e+1]]; tsigma[1]=1; tsigma[n_]:= Times @@ f @@@ FactorInteger[n]; s[n_] := tsigma[n] - n; seq={}; Do[m=s[n]; If[m>n && s[m]==n, AppendTo[seq, m]] ,{n,1,700000}]; seq
A322541
Lesser of semi-unitary amicable numbers pair: numbers (m, n) such that susigma(m) = susigma(n) = m + n, where susigma(n) is the sum of the semi-unitary divisors of n (A322485).
Original entry on oeis.org
114, 366, 1140, 3660, 3864, 5016, 11040, 15210, 16104, 16536, 18480, 44772, 57960, 67158, 68640, 68880, 142290, 142310, 155760, 196248, 198990, 240312, 248040, 275520, 278160, 308220, 322080, 326424, 339822, 348840, 352632, 366792, 462330, 485760, 607920
Offset: 1
114 is in the sequence since it is the lesser of the amicable pair (114, 126): susigma(114) = susigma(126) = 114 + 126.
-
f[p_, e_] := (p^Floor[(e + 1)/2] - 1)/(p - 1) + p^e; s[n_] := If[n == 1, 1, Times @@ (f @@@ FactorInteger[n])] - n; seq = {}; Do[n = s[m]; If[n > m && s[n] == m, AppendTo[seq, m]], {m, 1, 1000000}]; seq
-
susigma(n) = {my(f = factor(n)); for (k=1, #f~, my(p=f[k, 1], e=f[k, 2]); f[k, 1] = (p^((e+1)\2) - 1)/(p-1) + p^e; f[k, 2] = 1; ); factorback(f); } \\ A322485
isok(n) = my(m=susigma(n)-n); (m > n) && (susigma(m) == n + m); \\ Michel Marcus, Dec 15 2018
A348344
Larger member of a noninfinitary amicable pair: numbers (k, m) such that nisigma(k) = m and nisigma(m) = k, where nisigma(k) is the sum of the noninfinitary divisors of k (A348271).
Original entry on oeis.org
448, 2032, 8128, 7168, 24384, 41984, 130048, 41940480, 102222432, 221316608, 34359738352
Offset: 1
448 is a term since A348271(448) = 336 and A348271(336) = 448.
-
f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := DivisorSigma[1,n] - isigma[n]; seq={}; Do[m=s[n]; If[m>n && s[m]==n, AppendTo[seq, m]], {n,1,10^4}]; seq
A357496
Greater of a pair of amicable numbers k < m such that s(k) = m and s(m) = k, where s(k) = A162296(k) - k is the sum of aliquot divisors of k that have a square factor.
Original entry on oeis.org
1136, 11696, 22256, 25472, 43424, 73664, 131355, 304336, 267968, 492608, 612704, 674920, 640305, 788697, 691292, 705344, 723392, 813728, 809776, 1117395, 1258335, 1559696, 1518570, 1598368, 1821376, 2218250, 2058944, 2678752, 2744288, 2765024, 2848864, 2610656, 3134224
Offset: 1
1136 is a term since s(1136) = 880 and s(880) = 1136.
-
s[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1) - n]; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 2, 3*10^6}]; seq
A371420
Greater member of Carmichael's variant of amicable pair: numbers k < m such that s(k) = m and s(m) = k, where s(k) = A371418(k).
Original entry on oeis.org
14, 62, 124, 189, 254, 508, 2032, 16382, 32764, 131056, 262142, 524284, 524224, 1048574, 2097148, 2097136, 8388592, 8388544, 33554368, 536866816, 2147479552, 4294967294, 8589934588, 34359738352, 34359672832, 137438953408
Offset: 1
14 is a term since A371418(14) = 12 < 14, and A371418(12) = 14.
-
r[n_] := n/FactorInteger[n][[1, 1]]; s[n_] := r[DivisorSigma[1, n]]; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 1, 10^6}]; seq
-
f(n) = {my(s = sigma(n)); if(s == 1, 1, s/factor(s)[1, 1]);}
lista(nmax) = {my(m); for(n = 1, nmax, m = f(n); if(m > n && f(m) == n, print1(m, ", ")));}
A348603
Larger member of a nonexponential amicable pair: numbers (k, m) such that nesigma(k) = m and nesigma(m) = k, where nesigma(k) is the sum of the nonexponential divisors of k (A160135).
Original entry on oeis.org
204, 19332, 168730, 1099390, 1292570, 1598470, 2062570, 2429030, 3077354, 3903012, 4488910, 6135962, 5504110, 5812130, 7158710, 8221598, 9627915, 10893230, 10043690, 11049730, 10273670, 18087818, 19150222, 17578785, 23030090, 32174506, 35997346, 40117714, 39944086
Offset: 1
204 is a term since A160135(204) = 198 and A160135(198) = 204.
-
esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; s[n_] := DivisorSigma[1, n] - esigma[n]; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 1, 1.7*10^6}]; seq
Showing 1-6 of 6 results.
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