login
a(n) = index of the least prime divisor of n which has an odd exponent, or 0 if n is a perfect square.
4

%I #16 May 17 2017 17:54:11

%S 0,1,2,0,3,1,4,1,0,1,5,2,6,1,2,0,7,1,8,3,2,1,9,1,0,1,2,4,10,1,11,1,2,

%T 1,3,0,12,1,2,1,13,1,14,5,3,1,15,2,0,1,2,6,16,1,3,1,2,1,17,2,18,1,4,0,

%U 3,1,19,7,2,1,20,1,21,1,2,8,4,1,22,3,0,1,23,2,3,1,2,1,24,1,4,9,2,1,3,1,25,1,5,0,26,1,27,1,2

%N a(n) = index of the least prime divisor of n which has an odd exponent, or 0 if n is a perfect square.

%H Antti Karttunen, <a href="/A277707/b277707.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) is odd, then a(n) = A055396(n), otherwise a(n) = a(A028234(n)).

%F a(n) = A055396(A007913(n)).

%e For n = 8 = 2*2*2 = prime(1)^3, the exponent of the least (and the only) prime factor 2 is 3, an odd number, thus a(8) = 1 as 2 = prime(1).

%o (Scheme, two implementations)

%o (definec (A277707 n) (cond ((= 1 n) 0) ((odd? (A067029 n)) (A055396 n)) (else (A277707 (A028234 n)))))

%o (define (A277707 n) (A055396 (A007913 n)))

%o (PARI) a(n) = my(f = factor(core(n))); if (!#f~, 0, primepi(vecmin(f[,1]))); \\ _Michel Marcus_, Oct 30 2016

%o (Python)

%o from sympy import primepi, isprime, primefactors

%o from sympy.ntheory.factor_ import core

%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 a(n): return a055396(core(n)) # _Indranil Ghosh_, May 17 2017

%Y Cf. A007913, A028234, A055396, A067029.

%Y Cf. A000290 (after its initial zero-term gives the positions of zeros in this sequence).

%Y Cf. also A277708, A277697.

%K nonn

%O 1,3

%A _Antti Karttunen_, Oct 28 2016