cp's OEIS Frontend

A061395 Let p be the largest prime factor of n; if p is the k-th prime then set a(n) = k; a(1) = 0 by convention.

%I A061395 #78 May 01 2025 23:30:47
%S A061395 0,1,2,1,3,2,4,1,2,3,5,2,6,4,3,1,7,2,8,3,4,5,9,2,3,6,2,4,10,3,11,1,5,
%T A061395 7,4,2,12,8,6,3,13,4,14,5,3,9,15,2,4,3,7,6,16,2,5,4,8,10,17,3,18,11,4,
%U A061395 1,6,5,19,7,9,4,20,2,21,12,3,8,5,6,22,3,2,13,23,4,7,14,10,5,24,3,6,9,11,15
%N A061395 Let p be the largest prime factor of n; if p is the k-th prime then set a(n) = k; a(1) = 0 by convention.
%C A061395 Records occur at the primes. - _Robert G. Wilson v_, Dec 30 2007
%C A061395 For n > 1: length of n-th row in A067255. - _Reinhard Zumkeller_, Jun 11 2013
%C A061395 a(n) = the largest part of the partition having Heinz number n. We define the Heinz number of a partition p = [p_1, p_2, ..., p_r] as Product(p_j-th prime, j=1...r) (concept used by _Alois P. Heinz_ in A215366 as an "encoding" of a partition). For example, for the partition [1, 1, 2, 4, 10] we get 2*2*3*7*29 = 2436. Example: a(20) = 3; indeed, the partition having Heinz number 20 = 2*2*5 is [1,1,3]. - _Emeric Deutsch_, Jun 04 2015
%H A061395 Álvar Ibeas, <a href="/A061395/b061395.txt">Table of n, a(n) for n = 1..100000</a> (first 1000 terms from Harry J. Smith)
%H A061395 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A061395 A000040(a(n)) = A006530(n); a(n) = A049084(A006530(n)). - _Reinhard Zumkeller_, May 22 2003
%F A061395 A243055(n) = a(n) - A055396(n). - _Antti Karttunen_, Mar 07 2017
%F A061395 a(n) = A000720(A006530(n)). - _Alois P. Heinz_, Mar 05 2020
%F A061395 a(n) = A029837(A087207(n)+1). - _Flávio V. Fernandes_, Apr 24 2025
%e A061395 a(20) = 3 since the largest prime factor of 20 is 5, which is the 3rd prime.
%p A061395 with(numtheory):
%p A061395 a:= n-> pi(max(1, factorset(n)[])):
%p A061395 seq(a(n), n=1..100);  # _Alois P. Heinz_, Aug 03 2013
%t A061395 Insert[Table[PrimePi[FactorInteger[n][[ -1]][[1]]], {n, 2, 120}], 0, 1] (* _Stefan Steinerberger_, Apr 11 2006 *)
%t A061395 f[n_] := PrimePi[ FactorInteger@n][[ -1, 1]]; Array[f, 94] (* _Robert G. Wilson v_, Dec 30 2007 *)
%o A061395 (PARI) a(n) = if (n==1, 0, primepi(vecmax(factor(n)[,1]))); \\ _Michel Marcus_, Nov 14 2022
%o A061395 (Haskell)
%o A061395 a061395 = a049084 . a006530  -- _Reinhard Zumkeller_, Jun 11 2013
%o A061395 (Python)
%o A061395 from sympy import primepi, primefactors
%o A061395 def a(n): return 0 if n==1 else primepi(primefactors(n)[-1])
%o A061395 print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, May 14 2017
%Y A061395 Cf. A000720, A006530, A055396, A061394, A133674, A243055.
%Y A061395 Cf. A029837, A087207.
%K A061395 easy,nice,nonn
%O A061395 1,3
%A A061395 _Henry Bottomley_, Apr 30 2001
%E A061395 Definition reworded by _N. J. A. Sloane_, Jul 01 2008