A277885 - OEIS

%I #22 Nov 19 2024 22:11:43

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A277885/b277885.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Pri#prime_indices">Index entries for sequences computed from prime indices</a>.

%F 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.]

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

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

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

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

%o (Python)

%o from sympy import factorint, primepi, isprime, primefactors

%o def a049084(n): return primepi(n)*(1*isprime(n))

%o def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))

%o def a028234(n):

%o     f = factorint(n)

%o     return 1 if n==1 else n/(min(f)**f[min(f)])

%o def a067029(n):

%o     f=factorint(n)

%o     return 0 if n==1 else f[min(f)]

%o def a(n): return 0 if n==1 else a055396(n) if a067029(n)>1 else a(a028234(n)) # _Indranil Ghosh_, May 15 2017

%o (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

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

%Y Cf. A277697.

%Y Cf. A005117 (gives the positions of zeros).

%K nonn

%O 1,9

%A _Antti Karttunen_, Nov 08 2016