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First terms with binary weights (A000120) w = 1..9 are: 1, 5, 14, 141, 4111, 25676, 41674, 1094530, 423297.

Antti Karttunen, <a href="/A339906/b339906.txt">Table of n, a(n) for n = 1..514</a>

Terms of (1/2)*A048675(A339907(i)), for i >= 1, sorted into ascending order.

Cf. A000010, A001222, A019565, A048675, A339812, A339902, A339907.

Cf. A000010, A001222, A019565, A339812, A339902, A339907.

Cf. A000079 (a subsequence).

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.

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).

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).

allocated Numbers k for Antti Karttunenwhich A339812(2k) >= A339902(k).

1, 2, 4, 5, 8, 9, 10, 14, 16, 18, 32, 64, 65, 72, 84, 128, 129, 132, 136, 141, 145, 170, 256, 258, 261, 385, 448, 512, 516, 578, 642, 912, 1024, 1040, 1049, 1160, 1352, 2048, 4096, 4097, 4100, 4111, 4160, 4652, 4675, 4864, 5124, 5280, 8192, 8193, 8194, 8195, 8196, 8200, 8214, 8216, 8258, 8320, 8329, 8468, 8704

1,2

(PARI)

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

A339812(n) = bigomega(A019565(n)-1);

A339902(n) = { my(s=0, p=2); while(n>0, p = nextprime(1+p); if(n%2, s += bigomega(p-1)); n >>= 1); (s); };

isA339906(n) = (A339812(2*n) >= A339902(n));

(PARI)

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

isA339906(n) = { my(x=A019565(2*n)); (bigomega(eulerphi(x))<=bigomega(x-1)); };

Cf. A339907.

Cf. also A339816.

allocated

nonn

Antti Karttunen, Dec 21 2020

approved

editing

allocated for Antti Karttunen

allocated

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