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approved

editing

proposed

A324861(n) = #binary(A324876(n)); \\ Needs also code from A324876.

A324863(n) = { my(m=0, w, c=0); fordiv(n, d, w=A324861(d); if(w>=m, if(w==m, c++, c=1; m=w))); (m); };

A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552

A324866(n) = { my(k=A156552(n)); bitor(k, (A323243(n)-k)); }; \\ Needs also code from A323243.

A324863(n) = #binary(A324866(n));

Cf. A156552, A252464, A324863, A324866, A324871, A324872.

Question: Are there any other terms than 0's and 1's ? There are only 201 nonzero values among the first 10000 terms and they are all 1's ?.

Antti Karttunen, <a href="/A324870/b324870.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)

Question: Are there any other terms than 0's and 1's ?

A324871 gives the numbers n where a(n) <> 0. The first such number which is not a square is 187 = 11*17.

A324871 gives the n where a(n) <> 0. The first such number which is not a nonsquaresquare is 187 = 11*17.

Antti Karttunen: Longish data section because sparse data.

allocated for Antti Karttunen

a(n) = A324863(n) - A252464(n).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

1

A324871 gives the n where a(n) <> 0. The first such nonsquare is 187 = 11*17.

<a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

<a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

<a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

a(n) = A324863(n) - A252464(n).

(PARI)

A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));

A252464(n) = if(1==n, 0, (bigomega(n) + A061395(n) - 1));

A324861(n) = #binary(A324876(n)); \\ Needs also code from A324876.

A324863(n) = { my(m=0, w, c=0); fordiv(n, d, w=A324861(d); if(w>=m, if(w==m, c++, c=1; m=w))); (m); };

A324870(n) = (A324863(n) - A252464(n));

allocated

nonn

Antti Karttunen, Mar 21 2019

approved

editing

allocated for Antti Karttunen

allocated

approved