cp's OEIS Frontend

A339906 Numbers k for which A339812(2k) >= A339902(k).

%I A339906 #9 Dec 24 2020 21:22:32
%S A339906 1,2,4,5,8,9,10,14,16,18,32,64,65,72,84,128,129,132,136,141,145,170,
%T A339906 256,258,261,385,448,512,516,578,642,912,1024,1040,1049,1160,1352,
%U A339906 2048,4096,4097,4100,4111,4160,4652,4675,4864,5124,5280,8192,8193,8194,8195,8196,8200,8214,8216,8258,8320,8329,8468,8704
%N A339906 Numbers k for which A339812(2k) >= A339902(k).
%C A339906 Terms of (1/2)*A048675(A339907(i)), for i >= 1, sorted into ascending order.
%C A339906 The first term not present in A339816 is 10, the second is 642; the first term of A339816 not present here is 12, the second is 21.
%C A339906 First terms with binary weights (A000120) w = 1..9 are: 1, 5, 14, 141, 4111, 25676, 41674, 1094530, 423297.
%H A339906 Antti Karttunen, <a href="/A339906/b339906.txt">Table of n, a(n) for n = 1..514</a>
%e A339906 10 ("1010" in binary) is present, because it encodes an odd squarefree number 5*11, for which phi(55) = 4*10 = 40, and bigomega(55-1) = 4 >= 4 = bigomega(40).
%e A339906 12 ("1100" in binary) is NOT present, because it encodes an odd squarefree number 7*11, for which phi(77) = 6*10 = 60, and bigomega(77-1) = 3 < 4 = bigomega(60).
%o A339906 (PARI)
%o A339906 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A339906 A339812(n) = bigomega(A019565(n)-1);
%o A339906 A339902(n) = { my(s=0, p=2); while(n>0, p = nextprime(1+p); if(n%2, s += bigomega(p-1)); n >>= 1); (s); };
%o A339906 isA339906(n) = (A339812(2*n) >= A339902(n));
%o A339906 (PARI)
%o A339906 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A339906 isA339906(n) = { my(x=A019565(2*n)); (bigomega(eulerphi(x))<=bigomega(x-1)); };
%Y A339906 Cf. A000010, A001222, A019565, A048675, A339812, A339902, A339907.
%Y A339906 Cf. A000079 (a subsequence).
%Y A339906 Cf. also A339816.
%K A339906 nonn
%O A339906 1,2
%A A339906 _Antti Karttunen_, Dec 21 2020