cp's OEIS Frontend

A064372 Additive function a(n) defined by the recursive formula a(1)=1 and a(p^k)=a(k) for any prime p.

%I A064372 #35 Dec 22 2021 07:43:20
%S A064372 1,1,1,1,1,2,1,1,1,2,1,2,1,2,2,1,1,2,1,2,2,2,1,2,1,2,1,2,1,3,1,1,2,2,
%T A064372 2,2,1,2,2,2,1,3,1,2,2,2,1,2,1,2,2,2,1,2,2,2,2,2,1,3,1,2,2,2,2,3,1,2,
%U A064372 2,3,1,2,1,2,2,2,2,3,1,2,1,2,1,3,2,2,2,2,1,3,2,2,2,2,2,2,1,2,2,2,1,3,1,2,3
%N A064372 Additive function a(n) defined by the recursive formula a(1)=1 and a(p^k)=a(k) for any prime p.
%C A064372 That is, if i, j, k, ... are relatively prime, then a(i*j*k*...) = a(i) + a(j) + a(k) + ... - _N. J. A. Sloane_, Nov 20 2007
%C A064372 Starts almost the same as A001221 (the number of distinct primes dividing n): the first twelve terms which are different are a(1), a(64), a(192), a(320), a(448), a(576), a(704), a(729), a(832), a(960), a(1024) and a(1088), since the first non-unitary values of n are a(6) and(10). - _Henry Bottomley_, Sep 23 2002
%C A064372 a(A164336(n)) = 1. - _Reinhard Zumkeller_, Aug 27 2011
%H A064372 T. D. Noe, <a href="/A064372/b064372.txt">Table of n, a(n) for n = 1..10000</a>
%H A064372 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A064372 a(n) = A106491(n) - A106490(n) = A106495(A106444(n)). - _Antti Karttunen_, May 09 2005
%F A064372 a(1) = 1, a(n) = Sum_{k=1..A001221(n)} a(A124010(n,k)) for n > 1. - _Reinhard Zumkeller_, Aug 27 2011
%e A064372 a(30) = a(5^1 * 3^1 * 2^1) = a(1) + a(1) + a(1) = 3.
%p A064372 a:= proc(n) option remember; `if`(n=1, 1,
%p A064372       add(a(i[2]), i=ifactors(n)[2]))
%p A064372     end:
%p A064372 seq(a(n), n=1..120);  # _Alois P. Heinz_, Aug 23 2020
%t A064372 a[1] = 1; a[n_] := a[n] = Plus @@ a /@ FactorInteger[n][[All, 2]]; Table[a[n], {n, 1, 105}] (* _Jean-François Alcover_, Sep 19 2012 *)
%o A064372 (Haskell)
%o A064372 a064372 1 = 1
%o A064372 a064372 n = sum $ map a064372 $ a124010_row n
%o A064372 -- _Reinhard Zumkeller_, Aug 27 2011
%Y A064372 Cf. A001221, A079553, A106444, A106490, A106491, A106495, A124010, A164336.
%K A064372 nonn,easy,nice
%O A064372 1,6
%A A064372 _Steven Finch_, Sep 26 2001