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
A292019
List of pairs of unitary amicable numbers (m, n) with record value of m/n.
Original entry on oeis.org
114, 126, 44772, 49308, 241110, 242730, 10254970, 10273670, 766292835, 766512285, 17454440640, 17454615360
Offset: 1
The ratios m/n are
114/126 = 0.90476...
44772/49308 = 0.90800...
241110/242730 = 0.99332...
10254970/10273670 = 0.99818...
766292835/766512285 = 0.99971...
17454440640/17454615360 = 0.99999...
A292020
List of pairs of unitary amicable numbers (m, n) with record low values of m/n.
Original entry on oeis.org
114, 126, 18018, 22302, 32130, 40446, 197340, 286500, 703972667580, 1057831128900
Offset: 1
The ratios m/n are
114/126 = 0.904...
18018/22302 = 0.807...
32130/40446 = 0.794...
197340/286500 = 0.688...
703972667580/1057831128900 = 0.665...
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