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A285316 Numbers n for which A019565(n) > n.

%I A285316 #19 May 02 2021 12:12:27
%S A285316 0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,
%T A285316 28,29,30,31,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
%U A285316 53,54,55,56,57,58,59,60,61,62,63,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87
%N A285316 Numbers n for which A019565(n) > n.
%H A285316 Antti Karttunen, <a href="/A285316/b285316.txt">Table of n, a(n) for n = 1..10000</a>
%t A285316 a019565[n_]:=Times @@ Prime@ Flatten@ Position[#, 1] &@ Reverse@ IntegerDigits[n, 2] ; Select[Range[0, 100], a019565[#]># &] (* _Indranil Ghosh_, Apr 18 2017, after _Michael De Vlieger_ *)
%o A285316 (PARI)
%o A285316 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from _M. F. Hasler_
%o A285316 isA285316(n) = (A019565(n) > n);
%o A285316 n=0; k=1; while(k <= 10000, if(isA285316(n),write("b285316.txt", k, " ", n);k=k+1); n=n+1);
%o A285316 (Scheme) ;; with _Antti Karttunen_'s IntSeq-library
%o A285316 (define A285316 (MATCHING-POS 1 0 (lambda (n) (> (A019565 n) n))))
%o A285316 (Python)
%o A285316 from operator import mul
%o A285316 from sympy import prime
%o A285316 from functools import reduce
%o A285316 def a019565(n): return reduce(mul, (prime(i+1) for i, v in enumerate(bin(n)[:1:-1]) if v == '1')) if n > 0 else 1
%o A285316 print([n for n in range(101) if a019565(n)>n]) # _Indranil Ghosh_, Apr 18 2017, after _Chai Wah Wu_
%Y A285316 Complement: A285315.
%Y A285316 Cf. A019565.
%K A285316 nonn
%O A285316 1,3
%A A285316 _Antti Karttunen_, Apr 18 2017