A277885 - OEIS

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A277885

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

6

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,9

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from prime indices.

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.

MATHEMATICA

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

PROG

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

(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

(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

CROSSREFS

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

Cf. A005117 (gives the positions of zeros).

Sequence in context: A219486 A284574 A206499 * A333842 A334109 A373591

Adjacent sequences: A277882 A277883 A277884 * A277886 A277887 A277888

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 08 2016

STATUS

approved