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%I #9 Nov 29 2019 04:02:22
%S 54,135,1122,1386,2244,2805,3366,3927,4488,5301,12369,15318,20445,
%T 22977,24534,28623,44979,58941,74169,78588,98892,131454,153363,175272,
%U 197181,210693,213206,222132,240792,240999,270891,274122,304580,335038,350267
%N Numbers n such that (n / sum of digits of n) is a golden semiprime.
%H Amiram Eldar, <a href="/A108780/b108780.txt">Table of n, a(n) for n = 1..2595</a> (terms below 10^11)
%e 1122 is a term because 1122/6=187 and 187=11*17 and 11*phi-17 = 0.798373... < 1.
%t goldQ[n_] := Module[{f = FactorInteger[n]}, If[Length[f] != 2, False, If[Max[f[[;;,2]]] != 1, False, Abs[f[[2,1]] - f[[1,1]] * GoldenRatio] < 1]]]; sumDigits[n_] := Plus @@ IntegerDigits[n]; seqQ[n_] := Divisible[n, (sd = sumDigits[n])] && goldQ[n/sd]; Select[Range[360000], seqQ] (* _Amiram Eldar_, Nov 29 2019 *)
%Y Cf. A001101, A108540.
%K base,nonn
%O 1,1
%A _Jason Earls_, Jun 26 2005
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