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A061853 Difference between smallest prime not dividing n and smallest nondivisor of n. 2
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,30

COMMENTS

a(12m+6) is always positive since it involves subtracting 4 from a larger number; the first case where a term not of this form is positive is a(420).

Primorials from A002110(2)=6 onward seem to give the positions of records. - Antti Karttunen, Jul 28 2017

Difference between the smallest prime coprime to n and the smallest non-divisor of n. - Michael De Vlieger, Jul 28 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..30030

FORMULA

a(n) = A053669(n) - A007978(n).

EXAMPLE

a(29)=2-2=0; a(30)=7-4=3; a(420)=11-8=3.

PROG

(PARI) a(n) = {my(f = factor(n), d = divisors(f), res, p = 2, i = 1, j); while(i<=#f~ && f[i, 1]==p, i++; p = nextprime(p+1)); res = p; for(j=2, #d, if(d[j]!=j, return(res - d[j-1] - 1)))} \\ David A. Corneth, Jul 29 2017

(Python)

from sympy import nextprime

def a053669(n):

    p=2

    while n%p==0: p=nextprime(p)

    return p

def a007978(n):

    p=2

    while n%p==0: p+=1

    return p

def a(n): return a053669(n) - a007978(n)

print map(a, xrange(1, 101)) # Indranil Ghosh, Jul 29 2017

CROSSREFS

Cf. A002110, A007978, A053669.

Sequence in context: A169585 A045840 A181000 * A010104 A282673 A280051

Adjacent sequences:  A061850 A061851 A061852 * A061854 A061855 A061856

KEYWORD

nonn

AUTHOR

Henry Bottomley, May 10 2001

EXTENSIONS

Description corrected by Michael De Vlieger, Jul 28 2017

STATUS

approved

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Last modified February 21 19:30 EST 2019. Contains 320376 sequences. (Running on oeis4.)