A277885 a(n) = index of the least non-unitary prime divisor of n or 0 if no such prime-divisor exists.

0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 3, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 4, 3, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 3, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 4, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1

Offset: 1

Author

Antti Karttunen, Nov 08 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from prime indices.

Crossrefs

Cf. A008578, A028234, A032742, A055396, A067029, A249739.

Cf. A277697.

Cf. A005117 (gives the positions of zeros).

Programs

Mathematica

Table[PrimePi@ Min[Select[FactorInteger[n][[All, 1]], ! CoprimeQ[#, n/#] &] /. {} -> 0], {n, 120}] (* Michael De Vlieger, Nov 15 2016 *)

PARI

a(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 2] > 1, return(primepi(f[i, 1])))); 0;} \\ Amiram Eldar, Jul 28 2024

Python

from sympy import factorint, primepi, isprime, primefactors
def a049084(n): return primepi(n)*(1*isprime(n))
def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))
def a028234(n):
    f = factorint(n)
    return 1 if n==1 else n/(min(f)**f[min(f)])
def a067029(n):
    f=factorint(n)
    return 0 if n==1 else f[min(f)]
def a(n): return 0 if n==1 else a055396(n) if a067029(n)>1 else a(a028234(n)) # Indranil Ghosh, May 15 2017

Scheme

(definec (A277885 n) (cond ((= 1 n) 0) ((< 1 (A067029 n)) (A055396 n)) (else (A277885 (A028234 n)))))

Formula

a(1) = 0; for n > 1, if A067029(n) > 1, a(n) = A055396(n), otherwise a(n) = a(A028234(n)). [One may use A032742 instead of A028234 for recursing.]

A008578(1+a(n)) = A249739(n).

For n > 1, a(n) + A277697(n) > 0.