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A359830
Numbers k such that A048675(k) is not a multiple of 3.
2
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, 37, 39, 40, 41, 42, 43, 45, 46, 47, 49, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 66, 67, 70, 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
OFFSET
1,1
COMMENTS
Sequence is closed with respect to prime shifting: for any k present in the sequence, also A003961(k) and A348717(k) are present.
PROG
(PARI)
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
isA359830(n) = !!(A048675(n)%3);
(Python)
from itertools import count, islice
from sympy import primepi, factorint
def A359830_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:sum(e<<primepi(p)-1 for p, e in factorint(n).items())%3, count(max(startvalue, 1)))
A359830_list = list(islice(A359830_gen(), 20)) # Chai Wah Wu, Jan 17 2023
CROSSREFS
Complement of A332820. Positions of 0's in A353350.
Union of A332821 and A332822.
Cf. A000040 (subsequence), A003961, A048675, A348717, A353348.
Sequence in context: A191919 A039055 A047504 * A088962 A047363 A191917
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 17 2023
STATUS
approved