A344028 -id:A344028 - cp's OEIS frontend

A344182 a(n) = A344026(n) XOR A344028(n).

0, 0, 0, 6, 0, 0, 5, 8, 0, 0, 0, 26, 15, 26, 18, 40, 0, 0, 0, 22, 0, 0, 63, 56, 9, 14, 31, 34, 82, 124, 119, 64, 0, 0, 0, 50, 0, 0, 45, 88, 0, 0, 0, 98, 99, 38, 234, 88, 29, 114, 29, 202, 35, 34, 136, 160, 162, 444, 406, 130, 393, 430, 452, 224, 0, 0, 0, 42, 0, 0, 97, 120, 0, 0, 0, 46, 215, 222, 130, 136, 0, 0, 0, 202

Offset: 0

Antti Karttunen, May 16 2021

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A003415, A003714 (positions of zeros), A005940, A069359, A344026, A344028.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359
A344182(n) = { my(u=A005940(1+n)); bitxor(A003415(u),A069359(u)); };

a(n) = A344026(n) XOR A344028(n) = A003415(A005940(1+n)) XOR A069359(A005940(1+n)).

A344026 Arithmetic derivative applied to the Doudna sequence: a(n) = A003415(A005940(1+n)).

Original entry on oeis.org

0, 1, 1, 4, 1, 5, 6, 12, 1, 7, 8, 16, 10, 21, 27, 32, 1, 9, 10, 24, 12, 31, 39, 44, 14, 45, 55, 60, 75, 81, 108, 80, 1, 13, 14, 32, 16, 41, 51, 68, 18, 59, 71, 92, 95, 123, 162, 112, 22, 77, 91, 140, 119, 185, 240, 156, 147, 275, 350, 216, 500, 297, 405, 192, 1, 15, 16, 48, 18, 61, 75, 92, 20, 87, 103, 124, 135, 165, 216

Offset: 0

Antti Karttunen, May 07 2021

Coincides with A344028 on Fibbinary numbers, A003714.

Antti Karttunen, Table of n, a(n) for n = 0..8192
Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A000079 (positions of ones), A003415, A003714, A005940.

Cf. also A344027, A344028, A344182.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A344026(n) = A003415(A005940(1+n));

a(2^n) = 1 for all n >= 0.

cp's OEIS Frontend

A344182 a(n) = A344026(n) XOR A344028(n).

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