cp's OEIS Frontend

A277698 a(n) = least unitary prime divisor of n or 1 if no such prime-divisor exists.

%I A277698 #19 Jul 28 2024 10:08:21
%S A277698 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,
%T A277698 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,
%U A277698 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
%N A277698 a(n) = least unitary prime divisor of n or 1 if no such prime-divisor exists.
%H A277698 Antti Karttunen, <a href="/A277698/b277698.txt">Table of n, a(n) for n = 1..10000</a>
%F A277698 a(n) = A008578(1+A277697(n)).
%F A277698 a(n) = A020639(A055231(n)). - _Amiram Eldar_, Jul 28 2024
%t A277698 Table[If[Length@ # == 0, 1, First@ #] &@ Select[FactorInteger[n][[All, 1]], GCD[#, n/#] == 1 &], {n, 105}] (* _Michael De Vlieger_, Oct 30 2016 *)
%o A277698 (Scheme) (define (A277698 n) (A008578 (+ 1 (A277697 n))))
%o A277698 (Python)
%o A277698 from sympy import factorint, prime, primepi, isprime, primefactors
%o A277698 def a049084(n): return primepi(n)*(1*isprime(n))
%o A277698 def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))
%o A277698 def a028234(n):
%o A277698     f = factorint(n)
%o A277698     return 1 if n==1 else n/(min(f)**f[min(f)])
%o A277698 def a067029(n):
%o A277698     f=factorint(n)
%o A277698     return 0 if n==1 else f[min(f)]
%o A277698 def a277697(n): return 0 if n==1 else a055396(n) if a067029(n)==1 else a277697(a028234(n))
%o A277698 def a008578(n): return 1 if n==1 else prime(n - 1)
%o A277698 def a(n): return a008578(1 + a277697(n)) # _Indranil Ghosh_, May 16 2017
%o A277698 (PARI) a(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 2] == 1, return(f[i, 1]))); 1;} \\ _Amiram Eldar_, Jul 28 2024
%Y A277698 Cf. A008578, A020639, A055231, A277697.
%Y A277698 Cf. A001694 (positions of ones).
%Y A277698 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).
%Y A277698 Differs from A134194 for the first time at n=18, where a(18) = 2, while A134194(18) = 3.
%K A277698 nonn
%O A277698 1,2
%A A277698 _Antti Karttunen_, Oct 28 2016