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1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 4, 2, 1, 2, 2, 4, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 4, 4, 2, 2, 2, 2, 4, 2, 2, 2, 1, 4, 4, 2, 2, 2, 4, 2, 3, 2, 2, 3, 2, 4, 4, 2, 2, 1, 2, 2, 4, 4, 2, 2, 2, 2, 6, 4, 2, 2, 2, 4, 2, 2, 3, 2, 3, 2, 4, 2, 2, 4
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internal format)
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OFFSET
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1,5
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COMMENTS
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Records 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 20, 24, 32, 36, 40, ... occur at n = 1, 5, 18, 30, 90, 210, 450, 630, 1890, 3150, 5670, 6930, 20790, 34650, 62370, ...
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LINKS
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FORMULA
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a(1) = a(2) = 1; for n > 2, a(n) = a(n/2) when n == 0 mod 4, a(n) = A051064(n) * a(n/2) when n == 2 mod 4, a(n) = a(A064989(n)), when n == 3 mod 6, otherwise a(n) = A055457(n) * a(A064989(n)).
For n > 2, let p = A252463(n). If p is even, then a(n) = a(p), if p is odd, then a(n) = A051064(p) * a(p).
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PROG
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(PARI)
A001227(n) = numdiv(n>>valuation(n, 2));
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
(PARI)
A051064(n) = if(n<1, 0, 1+valuation(n, 3));
(PARI)
A051064(n) = if(n<1, 0, 1+valuation(n, 3));
A055457(n) = if(n<1, 0, 1+valuation(n, 5));
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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