cp's OEIS Frontend

A241919 If n is a prime power, p_i^e, a(n) = i, (with a(1)=0), otherwise difference (i-j) of the indices of the two largest distinct primes p_i, p_j, i > j in the prime factorization of n: a(n) = A061395(n) - A061395(A051119(n)).

%I A241919 #17 May 20 2017 10:22:31
%S A241919 0,1,2,1,3,1,4,1,2,2,5,1,6,3,1,1,7,1,8,2,2,4,9,1,3,5,2,3,10,1,11,1,3,
%T A241919 6,1,1,12,7,4,2,13,2,14,4,1,8,15,1,4,2,5,5,16,1,2,3,6,9,17,1,18,10,2,
%U A241919 1,3,3,19,6,7,1,20,1,21,11,1,7,1,4,22,2,2,12,23
%N A241919 If n is a prime power, p_i^e, a(n) = i, (with a(1)=0), otherwise difference (i-j) of the indices of the two largest distinct primes p_i, p_j, i > j in the prime factorization of n: a(n) = A061395(n) - A061395(A051119(n)).
%C A241919 See A242411 and A241917 for other variants.
%H A241919 Antti Karttunen, <a href="/A241919/b241919.txt">Table of n, a(n) for n = 1..10000</a>
%F A241919 a(n) = A061395(n) - A061395(A051119(n)).
%o A241919 (Scheme) (define (A241919 n) (- (A061395 n) (A061395 (A051119 n))))
%o A241919 (Haskell)
%o A241919 a241919 1 = 0
%o A241919 a241919 n = i - j where
%o A241919             (i:j:_) = map a049084 $ reverse (1 : a027748_row n)
%o A241919 -- _Reinhard Zumkeller_, May 15 2014
%o A241919 (Python)
%o A241919 from sympy import factorint, primefactors, primepi
%o A241919 def a061395(n): return 0 if n==1 else primepi(primefactors(n)[-1])
%o A241919 def a053585(n):
%o A241919     if n==1: return 1
%o A241919     p = primefactors(n)[-1]
%o A241919     return p**factorint(n)[p]
%o A241919 def a051119(n): return n/a053585(n)
%o A241919 def a(n): return a061395(n) - a061395(a051119(n)) # _Indranil Ghosh_, May 19 2017
%Y A241919 Cf. A241917, A242411, A051119, A061395, A122111.
%Y A241919 Cf. A049084, A027748.
%K A241919 nonn
%O A241919 1,3
%A A241919 _Antti Karttunen_, May 13 2014