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A277698 a(n) = Least unitary prime divisor of n or 1 if no such prime-divisor exists. 4
1, 2, 3, 1, 5, 2, 7, 1, 1, 2, 11, 3, 13, 2, 3, 1, 17, 2, 19, 5, 3, 2, 23, 3, 1, 2, 1, 7, 29, 2, 31, 1, 3, 2, 5, 1, 37, 2, 3, 5, 41, 2, 43, 11, 5, 2, 47, 3, 1, 2, 3, 13, 53, 2, 5, 7, 3, 2, 59, 3, 61, 2, 7, 1, 5, 2, 67, 17, 3, 2, 71, 1, 73, 2, 3, 19, 7, 2, 79, 5, 1, 2, 83, 3, 5, 2, 3, 11, 89, 2, 7, 23, 3, 2, 5, 3, 97, 2, 11, 1, 101, 2, 103, 13, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

a(n) = A008578(1+A277697(n)).

MATHEMATICA

Table[If[Length@ # == 0, 1, First@ #] &@ Select[FactorInteger[n][[All, 1]], GCD[#, n/#] == 1 &], {n, 105}] (* Michael De Vlieger, Oct 30 2016 *)

PROG

(Scheme) (define (A277698 n) (A008578 (+ 1 (A277697 n))))

(Python)

from sympy import factorint, prime, 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 a277697(n): return 0 if n==1 else a055396(n) if a067029(n)==1 else a277697(a028234(n))

def a008578(n): return 1 if n==1 else prime(n - 1)

def a(n): return a008578(1 + a277697(n)) # Indranil Ghosh, May 16 2017

CROSSREFS

Cf. A008578, A277697.

Cf. A001694 (positions of ones).

Cf. A080368 for a variant which gives 0's instead of 1's for numbers with no unitary prime divisors and also A277708 (the least prime factor with an odd exponent).

Differs from A134194 for the first time at n=18, where a(18) = 2, while A134194(18) = 3.

Sequence in context: A340078 A126773 A326691 * A134194 A308707 A158584

Adjacent sequences:  A277695 A277696 A277697 * A277699 A277700 A277701

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 28 2016

STATUS

approved

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Last modified September 18 22:34 EDT 2021. Contains 347548 sequences. (Running on oeis4.)