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A324384 a(n) = gcd(n, A276154(n)), where A276154 is the primorial base left shift. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to primorial base

FORMULA

a(n) = gcd(n, A276154(n)).

PROG

(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)); };

A276154(n) = if(!n, n, (A276152(n) + A276154(A276151(n))));

\\ Alternatively, A276154 can be defined with A276085, A276086 and A003961:

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; };

A276154(n) = A276085(A003961(A276086(n)));

A324384(n) = gcd(n, A276154(n));

CROSSREFS

Cf. A002110, A049345, A276085, A276086, A276151, A276152, A276154, A323879, A324198, A324350, A324351.

Sequence in context: A128707 A257022 A214721 * A329641 A329638 A322036

Adjacent sequences:  A324381 A324382 A324383 * A324385 A324386 A324387

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 26 2019

STATUS

approved

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Last modified May 25 08:26 EDT 2020. Contains 334585 sequences. (Running on oeis4.)