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 A307962 Lesser of coreful amicable numbers pair: numbers (m, n) such that csigma(m) = csigma(n) = m + n, where csigma(n) is the sum of the coreful divisors of n (A057723). 4
 1718200, 4818880, 5154600, 12027400, 14456640, 22336600, 29209400, 32645800, 33732160, 36082200, 39518600, 49827800, 53264200, 62645440, 63573400, 67009800, 70446200, 73882600, 80755400, 81920960, 87628200, 91064600, 91558720, 97937400, 101196480, 101373800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The larger counterparts are in A307963. If (m, n) is an amicable pair (A259180), then the pair (m*k, n*k) with k=rad(m*n) is a coreful amicable pair (rad(i)=A007947(i) is the squarefree kernel of i), and so are all the pairs (m*k*s, n*k*s) where s is a squarefree number with gcd(s, k) = 1. Proof: k = rad(m*n) = rad(m)*rad(n)/rad(gcd(m,n)), csigma(m*k) = csigma(m*rad(m)*j) where j = rad(n)/rad(gcd(m,n)) is squarefree and coprime to m*rad(m), so csigma(m*k) = j * csigma(m*rad(m)) = j * rad(m)* sigma(m) = rad(m)*rad(n)/rad(gcd(m,n)) * sigma(m) = rad(m)*rad(n)/rad(gcd(m,n)) * (n+m) = k *(n+m) = csigma(n*k). LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 MATHEMATICA f[p_, e_] := (p^(e+1)-1)/(p-1)-1; csigma[1]=1; csigma[n_] := Times @@ (f @@@ FactorInteger[n]); s={}; Do[m = csigma[n] - n; If[m > n && csigma[m] - m == n, AppendTo[s, n]], {n, 1, 10^8}]; s CROSSREFS Cf. A007947, A057723, A063990, A259180, A307958, A307959, A307963. Sequence in context: A234341 A207796 A235847 * A257382 A233633 A151639 Adjacent sequences: A307959 A307960 A307961 * A307963 A307964 A307965 KEYWORD nonn AUTHOR Amiram Eldar, May 08 2019 EXTENSIONS Wrong terms corrected by Amiram Eldar, Dec 02 2019 STATUS approved

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Last modified August 5 18:18 EDT 2024. Contains 374954 sequences. (Running on oeis4.)