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A347870 a(n) = A003415(sigma(n)) mod 2, where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n. 19
0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1
COMMENTS
If a(k) = 0 for all terms k of A342923, then there cannot be any odd perfect numbers, as k + 3*A003415(k) is odd for any k of the form 4u+2. See comments in A005820 and A235991, also in A347887.
LINKS
FORMULA
a(n) = A000035(A342925(n)) = A165560(A000203(n)).
a(n) = A000035(n) XOR A347871(n).
MATHEMATICA
ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); a[n_] := Mod[ad[DivisorSigma[1, n]], 2]; Array[a, 105] (* Amiram Eldar, Sep 18 2021 *)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342925(n) = A003415(sigma(n));
A347870(n) = (A342925(n)%2);
CROSSREFS
Characteristic function of A347877, while its complement A347878 gives the positions of zeros.
Sequence in context: A288741 A341684 A327183 * A188967 A090171 A316832
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 17 2021
STATUS
approved

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Last modified July 23 23:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)