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A324817
a(n) = sign(A323244(n))*A001511(A323244(n)), with a(n) = 0 if A323244(n) = 0.
3
0, 1, 1, 2, 1, 3, 1, 2, 0, 1, 1, 2, 1, 5, 2, 2, 1, 3, 1, 2, -1, 2, 1, 2, -3, 2, 3, 2, 1, 2, 1, 2, 2, 2, -2, 2, 1, 9, -3, 2, 1, 3, 1, 2, 4, 2, 1, 2, -3, 1, 4, 2, 1, 3, -1, 2, -3, 3, 1, 2, 1, 2, 5, 2, 2, 2, 1, 2, 2, 4, 1, 2, 1, 2, 2, 2, -2, 2, 1, 2, -3, 2, 1, 2, -4, 2, -3, 2, 1, 3, -1, 2, 2, 2, -3, 2, 1, 1, -3, 2, 1, 3, 1, 2, -3
OFFSET
1,4
FORMULA
If A323244(n) = 0, then a(n) = 0, otherwise a(n) = sign(A323244(n)) * A001511(A323244(n)).
a(p) = 1 for all primes p.
PROG
(PARI)
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 by David A. Corneth
A323244(n) = ((2*A156552(n))-A323243(n)); \\ Needs also code from A323243.
A001511ext(n) = if(!n, n, sign(n)*(1+valuation(n, 2))); \\ Like A001511 but gives 0 for 0 and -A001511(-n) for negative numbers.
A324817(n) = A001511ext(A323244(n));
KEYWORD
sign
AUTHOR
Antti Karttunen, Mar 17 2019
STATUS
approved