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%I #13 Jul 27 2023 15:23:21
%S 7,10,20,40,49,50,80,100,160,200,250,320,343,400,500,640,800,1000,
%T 1250,1280,1600,2000,2401,2500,2560,3200,4000,5000,5120,6250,6400,
%U 8000,10000,10240,12500,12800,16000,16807,20000,20480,25000,25600,31250,32000,40000,40960
%N Numbers whose sum of (distinct) prime divisors (A008472) equals 7.
%H Amiram Eldar, <a href="/A363292/b363292.txt">Table of n, a(n) for n = 1..1000</a>
%F Union of A000420 = {7^k ; k > 0} and A033846 = {2^j*5^k ; j, k > 0}.
%F Sum_{n>=1} 1/a(n) = 5/12. - _Amiram Eldar_, Jul 27 2023
%t seq[max_] := Union[Join[7^Range[Floor[Log[7, max]]], Flatten@ Table[2^i*5^j, {i, 1, Log2[max]}, {j, 1, Log[5, max/2^i]}]]]; seq[40000] (* _Amiram Eldar_, Jul 27 2023 *)
%o (PARI) select( {is_A363292(n)=vecsum(factor(n,0)[,1])==7}, [1..13^4]) \\ alternatively: [n | n<-[1..13^4], A008472(n)==7]
%Y Cf. A008472 (sopf), A000420 (7^n), A033846 (2^m*5^n), A362948 (A008472 = 5).
%K nonn,easy
%O 1,1
%A _M. F. Hasler_, Jul 20 2023
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