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A359830 Numbers k such that A048675(k) is not a multiple of 3.

%I A359830 #9 Jan 18 2023 02:21:37
%S A359830 2,3,4,5,7,9,10,11,12,13,16,17,18,19,21,22,23,24,25,28,29,30,31,32,34,
%T A359830 37,39,40,41,42,43,45,46,47,49,52,53,54,55,56,57,59,60,61,62,66,67,70,
%U A359830 71,72,73,75,76,78,79,80,81,82,83,85,87,88,89,91,94,96,97,98,99,100,101,102,103,104,105,107,108
%N A359830 Numbers k such that A048675(k) is not a multiple of 3.
%C A359830 Sequence is closed with respect to prime shifting: for any k present in the sequence, also A003961(k) and A348717(k) are present.
%H A359830 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A359830 (PARI)
%o A359830 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A359830 isA359830(n) = !!(A048675(n)%3);
%o A359830 (Python)
%o A359830 from itertools import count, islice
%o A359830 from sympy import primepi, factorint
%o A359830 def A359830_gen(startvalue=1): # generator of terms >= startvalue
%o A359830     return filter(lambda n:sum(e<<primepi(p)-1 for p,e in factorint(n).items())%3,count(max(startvalue,1)))
%o A359830 A359830_list = list(islice(A359830_gen(),20)) # _Chai Wah Wu_, Jan 17 2023
%Y A359830 Complement of A332820. Positions of 0's in A353350.
%Y A359830 Union of A332821 and A332822.
%Y A359830 Cf. A000040 (subsequence), A003961, A048675, A348717, A353348.
%K A359830 nonn
%O A359830 1,1
%A A359830 _Antti Karttunen_, Jan 17 2023