A339816 - OEIS

%I #10 Dec 20 2020 16:45:04

%S 1,2,4,5,8,9,12,14,16,18,21,32,64,65,68,72,84,128,129,132,136,138,141,

%T 145,159,170,192,204,208,256,258,261,324,385,448,462,512,513,515,516,

%U 520,536,576,578,581,640,705,723,776,908,912,1024,1036,1040,1049,1160,1172,1280,1352,1537,1600,1609,1666,1732,1795,2048

%N Numbers k for which A339814(k) >= A339822(k).

%C Terms of (1/2)*A048675(A339817(i)), for i = 2.., sorted into ascending order.

%C First occurrences of terms with binary weight (A000120) w = 1..19 are at n=1, 4, 8, 23, 50, 25, 125, 136, 176, 502, 749, 1142, 791, 1882, 2913, 4327, 17979, 16991, 12441. The terms themselves are: 1, 5, 14, 141, 908, 159, 8921, 9948, 18390, 175449, 400237, 1223389, 441805, 3234271, 28743379, 53892047, 1631024969, 1331412056, 725475951.

%H Antti Karttunen, <a href="/A339816/b339816.txt">Table of n, a(n) for n = 1..19468</a>

%o (PARI)

%o A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };

%o isA339816(n) = { my(x=A019565(2*n)); (valuation(eulerphi(x),2)<=valuation(x-1,2)); };

%Y Positions of zeros and negative terms in A339815.

%Y Cf. A000010, A000120, A007814, A019565, A048675, A339814, A339817, A339822.

%Y Cf. A000079 (a subsequence).

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 19 2020