A061853 Difference between smallest prime not dividing n and smallest nondivisor of n.

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

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([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jul 29 2017

Crossrefs

Cf. A002110, A007978, A053669.

Sequence in context: A045840 A181000 A335453 * A010104 A282673 A327159

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