A126166 -id:A126166 - cp's OEIS frontend

A323754 Larger member of primitive exponential amicable pairs.

100548, 968436, 5027400, 48665232, 48421800, 468723024, 845775504, 938024640, 26989110720, 40792003200, 48200025744, 63433162800, 303008547060

Offset: 1

Amiram Eldar, Jan 26 2019

The lesser counterparts are in A323753.

a(14) <= 647935817256.

			(90972 = 2^2*3^2*7*19^2, 100548 = 2^2*3^3*7^2*19) are a primitive pair since they are an exponential amicable pair (A126165, A126166) and they do not have a common prime divisor with multiplicity 1 in both.
(454860, 502740) = 5 * (90972, 100548) are not a primitive pair since 5 divides both of them only once.

Peter Hagis, Jr., Some Results Concerning Exponential Divisors, International Journal of Mathematics and Mathematical Sciences, Vol. 11, No. 2, (1988), pp. 343-350.
Jan Munch Pedersen, Known Exponential Amicable Pairs.

Cf. A051377, A054979, A049419, A054980, A126164, A126165, A126166, A126167, A323753.

rad[n_] := Times @@ First /@ FactorInteger[n]; pf[n_] := Denominator[n/rad[n]^2]; esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; es[n_] := esigma[n] - n; s = {}; Do[m = es[n]; If[m > n && es[m] == n && CoprimeQ[pf[n], pf[m]], AppendTo[s, m]], {n, 1, 10^7}]; s (* after Jean-François Alcover at A055231 and A051377 *)

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

Amiram Eldar, Oct 25 2021

nonn

The terms are ordered according to their smaller counterparts (A348602).

			204 is a term since A160135(204) = 198 and A160135(198) = 204.

Cf. A160135, A348601, A348602.

Similar sequences: A002046, A002953, A126166, A126170, A259039, A292981, A322542, A324709, A348344.

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

cp's OEIS Frontend

A323754 Larger member of primitive exponential amicable pairs.

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