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 A286470 a(n) = maximal gap between indices of successive primes in the prime factorization of n. 4
 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 3, 1, 0, 0, 1, 0, 2, 2, 4, 0, 1, 0, 5, 0, 3, 0, 1, 0, 0, 3, 6, 1, 1, 0, 7, 4, 2, 0, 2, 0, 4, 1, 8, 0, 1, 0, 2, 5, 5, 0, 1, 2, 3, 6, 9, 0, 1, 0, 10, 2, 0, 3, 3, 0, 6, 7, 2, 0, 1, 0, 11, 1, 7, 1, 4, 0, 2, 0, 12, 0, 2, 4, 13, 8, 4, 0, 1, 2, 8, 9, 14, 5, 1, 0, 3, 3, 2, 0, 5, 0, 5, 1, 15, 0, 1, 0, 2, 10, 3, 0, 6, 6, 9, 4, 16, 3, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(1) = 0, for n > 1, if A001221(n) = 1 [when n is a prime power], a(n) = 0, otherwise a(n) = max((A055396(A032742(n))-A055396(n)), a(A032742(n))). For all n >= 1, a(n) <= A243055(n). EXAMPLE For n = 70 = 2*5*7 = prime(1)*prime(3)*prime(4), the largest index difference occurs between prime(1) and prime(3), thus a(70) = 3-1 = 2. MATHEMATICA Table[If[Or[n == 1, PrimeNu@ n == 1], 0, Max@ Differences@ PrimePi[FactorInteger[n][[All, 1]]]], {n, 120}] (* Michael De Vlieger, May 16 2017 *) PROG (Scheme) (define (A286470 n) (cond ((or (= 1 n) (= 1 (A001221 n))) 0) (else (max (- (A055396 (A032742 n)) (A055396 n)) (A286470 (A032742 n)))))) (Python) from sympy import primepi, isprime, primefactors, divisors def a049084(n): return primepi(n)*(1*isprime(n)) def a055396(n): return 0 if n==1 else a049084(min(primefactors(n))) def x(n): return 1 if n==1 else divisors(n)[-2] def a(n): return 0 if n==1 or len(primefactors(n))==1 else max(a055396(x(n)) - a055396(n), a(x(n))) # Indranil Ghosh, May 17 2017 CROSSREFS Cf. A001221, A032742, A055396, A073490, A243055, A286455, A286471, A286472. Cf. A286469 (version which considers the index of the smallest prime as the initial gap). Cf. A000961 (positions of zeros). Differs from A242411 for the first time at n=70, where a(70) = 2, while A242411(70) = 1. Sequence in context: A087073 A297173 A242411 * A243055 A318371 A245151 Adjacent sequences:  A286467 A286468 A286469 * A286471 A286472 A286473 KEYWORD nonn AUTHOR Antti Karttunen, May 13 2017 EXTENSIONS Definition corrected by Zak Seidov, May 16 2017 STATUS approved

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Last modified September 18 11:42 EDT 2018. Contains 315130 sequences. (Running on oeis4.)