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Numbers k such that the sum of primes dividing k (with repetition) / smallest prime dividing k = largest prime dividing k.
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%I #17 Nov 03 2024 09:35:15

%S 4,27,30,70,84,286,308,440,528,594,646,728,884,945,1040,1170,1248,

%T 1404,1496,1748,1798,1976,3125,3128,3344,3526,3570,3762,3808,4250,

%U 4284,5100,5336,5440,5445,5586,6068,6120,6528,6650,7198,7344,7980,8084,8085,8262

%N Numbers k such that the sum of primes dividing k (with repetition) / smallest prime dividing k = largest prime dividing k.

%H Amiram Eldar, <a href="/A085702/b085702.txt">Table of n, a(n) for n = 1..10000</a>

%e 308 is a term: 308 = 2^2*7*11, 2+2+7+11 = 22, and 22/2 = 11.

%t q[k_] := Module[{f = FactorInteger[k]}, f[[1,1]] * f[[-1,1]] == Plus @@ Times @@@ f]; Select[Range[2, 10^4], q] (* _Amiram Eldar_, Nov 03 2024 *)

%o (PARI) is(k) = if(k > 1, my(f = factor(k)); f[1,1] * f[#f~, 1] == f[, 1]~ * f[, 2], 0); \\ _Amiram Eldar_, Nov 03 2024

%Y Cf. A001414, A006530, A020639.

%K easy,nonn

%O 1,1

%A _Jason Earls_, Jul 18 2003