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)).

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

Offset: 1

Author

Antti Karttunen, May 13 2014

Keywords

• nonn

Comments

See A242411 and A241917 for other variants.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

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

Cf. A049084, A027748.

Programs

Haskell

a241919 1 = 0
a241919 n = i - j where
            (i:j:_) = map a049084 $ reverse (1 : a027748_row n)
-- Reinhard Zumkeller, May 15 2014

Python

from sympy import factorint, primefactors, primepi
def a061395(n): return 0 if n==1 else primepi(primefactors(n)[-1])
def a053585(n):
    if n==1: return 1
    p = primefactors(n)[-1]
    return p**factorint(n)[p]
def a051119(n): return n/a053585(n)
def a(n): return a061395(n) - a061395(a051119(n)) # Indranil Ghosh, May 19 2017

Scheme

(define (A241919 n) (- (A061395 n) (A061395 (A051119 n))))

Formula

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