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A324384
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a(n) = gcd(n, A276154(n)), where A276154 is the primorial base left shift.
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3
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0, 1, 2, 1, 4, 1, 6, 1, 4, 1, 2, 11, 12, 1, 2, 1, 8, 1, 18, 1, 4, 7, 2, 1, 24, 1, 2, 1, 4, 1, 30, 1, 8, 1, 2, 7, 12, 1, 2, 1, 4, 1, 6, 1, 4, 1, 2, 1, 12, 1, 2, 1, 52, 1, 6, 1, 56, 1, 2, 1, 60, 1, 2, 1, 16, 1, 6, 1, 4, 1, 14, 1, 24, 1, 2, 1, 4, 1, 6, 1, 4, 1, 2, 1, 12, 1, 2, 1, 8, 1, 90, 1, 4, 1, 2, 1, 12, 1, 2, 1, 4, 1, 6, 1, 8, 1
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OFFSET
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0,3
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COMMENTS
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For a very few primes, a(p) > 1 (then by necessity a(p) = p). In range 2 .. 2^25 there are three: 2, 11, 119039.
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LINKS
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FORMULA
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PROG
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(PARI)
A276151(n) = { my(s=1); forprime(p=2, , if(n%p, return(n-s), s *= p)); };
A276152(n) = { my(s=1); forprime(p=2, , if(n%p, return(s*p), s *= p)); };
A002110(n) = prod(i=1, n, prime(i));
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };
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CROSSREFS
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Cf. A002110, A049345, A276085, A276086, A276151, A276152, A276154, A323879, A324198, A324350, A324351.
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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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