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 A292365 Abundant numbers n such that sigma(sigma(n) - 2*n) = sigma(n). 1

%I

%S 120,672,1740,7776,19260,20640,21384,21924,22428,25830,31440,55968,

%T 93024,101010,106140,143910,151164,198792,246510,309582,326196,411138,

%U 421596,428256,499464,523776,590112,639288,697158,870552,941094,958716,1060956,1068210,1087776,1100640,1105884,1269828

%N Abundant numbers n such that sigma(sigma(n) - 2*n) = sigma(n).

%C A005820 is a subsequence.

%C 101010 is the least squarefree term. For 6 <= k <= 8, the smallest squarefree terms with k prime factors are 101010 = 2*3*5*7*13*37, 35574630 = 2*3*5*7*13*83*157, and 401738610 = 2*3*5*7*13*31*47*101.

%H Amiram Eldar, <a href="/A292365/b292365.txt">Table of n, a(n) for n = 1..1210</a> (terms below 4*10^9)

%e 120 is a term because sigma(sigma(120) - 240) = sigma(360 - 240) = sigma(120).

%t Select[Range[1.3*^6], (d = DivisorSigma[1, #]; d > 2 # && DivisorSigma[1, d - 2 #] == d) &] (* _Giovanni Resta_, Sep 18 2017 *)

%o (PARI) s(n) = sigma(n);

%o isok(n) = s(n)>2*n && s(s(n)-2*n)==s(n);

%Y Cf. A000203, A005101, A005820.

%K nonn

%O 1,1

%A _Altug Alkan_, Sep 15 2017

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Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)