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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)).
10

%I #17 May 20 2017 10:22:31

%S 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 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 1,3,3,19,6,7,1,20,1,21,11,1,7,1,4,22,2,2,12,23

%N 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 See A242411 and A241917 for other variants.

%H Antti Karttunen, <a href="/A241919/b241919.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A061395(n) - A061395(A051119(n)).

%o (Scheme) (define (A241919 n) (- (A061395 n) (A061395 (A051119 n))))

%o (Haskell)

%o a241919 1 = 0

%o a241919 n = i - j where

%o (i:j:_) = map a049084 $ reverse (1 : a027748_row n)

%o -- _Reinhard Zumkeller_, May 15 2014

%o (Python)

%o from sympy import factorint, primefactors, primepi

%o def a061395(n): return 0 if n==1 else primepi(primefactors(n)[-1])

%o def a053585(n):

%o if n==1: return 1

%o p = primefactors(n)[-1]

%o return p**factorint(n)[p]

%o def a051119(n): return n/a053585(n)

%o def a(n): return a061395(n) - a061395(a051119(n)) # _Indranil Ghosh_, May 19 2017

%Y Cf. A241917, A242411, A051119, A061395, A122111.

%Y Cf. A049084, A027748.

%K nonn

%O 1,3

%A _Antti Karttunen_, May 13 2014