cp's OEIS Frontend

A286611 Numbers k for which A019565(k) <= A087207(k).

%I A286611 #11 Jul 31 2025 14:31:35
%S A286611 17,19,34,37,41,43,47,53,59,61,65,67,69,71,73,74,79,82,83,86,89,97,
%T A286611 101,103,106,107,109,113,118,122,127,129,131,134,137,139,141,142,145,
%U A286611 146,148,149,151,157,158,163,164,166,167,173,177,178,179,181,183,191,193,194,197,199,201,202,206,211,212
%N A286611 Numbers k for which A019565(k) <= A087207(k).
%C A286611 Any 2-cycle of A087207 and also any 2-cycle of A019565 (in which case A019565(x) = A087207(x) for both members of the cycle), if such cycles exist at all, must have the both of its members included in this sequence.
%H A286611 Antti Karttunen, <a href="/A286611/b286611.txt">Table of n, a(n) for n = 1..10000</a>
%H A286611 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A286611 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A286611 (PARI)
%o A286611 A007947(n) = factorback(factorint(n)[, 1]);
%o A286611 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; }; \\ After _Michel Marcus_
%o A286611 A087207(n) = A048675(A007947(n));
%o A286611 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 A286611 isA286611(n) = (A019565(n) <= A087207(n));
%o A286611 n=0; k=1; while(k <= 10000, n=n+1; if(isA286611(n),write("b286611.txt", k, " ", n);k=k+1));
%o A286611 (Scheme)
%o A286611 ;; With _Antti Karttunen_'s IntSeq-library.
%o A286611 (define A286611 (MATCHING-POS 1 1 (lambda (n) (<= (A019565 n) (A087207 n)))))
%Y A286611 Cf. A019565, A087207, A285315, A285316, A286609.
%Y A286611 Intersection with A286608 gives A286612.
%K A286611 nonn,base
%O A286611 1,1
%A A286611 _Antti Karttunen_, Jun 20 2017