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 A263297 The greater of bigomega(n) and maximal prime index in the prime factorization of n. 27
 0, 1, 2, 2, 3, 2, 4, 3, 2, 3, 5, 3, 6, 4, 3, 4, 7, 3, 8, 3, 4, 5, 9, 4, 3, 6, 3, 4, 10, 3, 11, 5, 5, 7, 4, 4, 12, 8, 6, 4, 13, 4, 14, 5, 3, 9, 15, 5, 4, 3, 7, 6, 16, 4, 5, 4, 8, 10, 17, 4, 18, 11, 4, 6, 6, 5, 19, 7, 9, 4, 20, 5, 21, 12, 3, 8, 5, 6, 22, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also: minimal m such that n is the product of at most m primes not exceeding prime(m). (Here the primes do not need to be distinct; cf. A263323.) By convention, a(1)=0, as 1 is the empty product. Those n with a(n) <= k fill a k-simplex whose 1-sides span from 0 to k. For a similar construction with distinct primes (hypercube), see A263323. Each nonnegative integer occurs finitely often; in particular: - Terms a(n) <= k occur A000984(k) = (2*k)!/(k!)^2 times. - The term a(n) = 0 occurs exactly once. - The term a(n) = k > 0 occurs exactly A051924(k) = (3*k-2)*C(k-1) times, where C(k)=A000108(k) are Catalan numbers. LINKS Antti Karttunen, Table of n, a(n) for n = 1..20000 FORMULA a(n) = max(A001222(n), A061395(n)). a(n) <= pi(n), with equality when n is 1 or prime. EXAMPLE a(6)=2 because 6 is the product of 2 primes (2*3), each not exceeding prime(2)=3. a(8)=3 because 8 is the product of 3 primes (2*2*2), each not exceeding prime(3)=5. a(11)=5 because 11 is prime(5). MAPLE seq(`if`(n=1, 0, max(pi(max(factorset(n))), bigomega(n))), n=1..80); # Peter Luschny, Oct 15 2015 MATHEMATICA f[n_] := Max[ PrimePi[ Max @@ First /@ FactorInteger@n], Plus @@ Last /@ FactorInteger@n]; Array[f, 80] PROG (PARI) a(n)=if(n<2, return(0)); my(f=factor(n)); max(vecsum(f[, 2]), primepi(f[#f~, 1])) \\ Charles R Greathouse IV, Oct 13 2015 CROSSREFS Cf. A000108, A000984, A001222, A051924, A061395, A263323, A325225, A331296 (ordinal transform), A331297. Sequence in context: A304464 A087050 A263323 * A163870 A327664 A155043 Adjacent sequences:  A263294 A263295 A263296 * A263298 A263299 A263300 KEYWORD nonn AUTHOR Alexei Kourbatov, Oct 13 2015 STATUS approved

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Last modified November 28 20:57 EST 2020. Contains 338755 sequences. (Running on oeis4.)