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 A064372 Additive function a(n) defined by the recursive formula a(1)=1 and a(p^k)=a(k) for any prime p. 12
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS 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 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 a(A164336(n)) = 1. - Reinhard Zumkeller, Aug 27 2011 LINKS T. D. Noe, Table of n, a(n) for n=1..10000 FORMULA a(n) = A106491(n) - A106490(n) = A106495(A106444(n)). - Antti Karttunen, May 09 2005 a(1) = 1, a(n) = sum(k=1..A001221(n), a(A124010(n,k)) ) for n > 1. - Reinhard Zumkeller, Aug 27 2011 EXAMPLE a(30) = a(5^1 * 3^1 * 2^1) = a(1) + a(1) + a(1) = 3. MATHEMATICA 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 *) PROG (Haskell) a064372 1 = 1 a064372 n = sum \$ map a064372 \$ a124010_row n -- Reinhard Zumkeller, Aug 27 2011 CROSSREFS Cf. A001221, A079553, A106444, A106490, A106491, A106495, A124010. Sequence in context: A087802 A079553 A001221 * A096825 A318369 A007875 Adjacent sequences:  A064369 A064370 A064371 * A064373 A064374 A064375 KEYWORD nonn,easy,nice AUTHOR Steven Finch, Sep 26 2001 STATUS approved

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Last modified August 11 04:00 EDT 2020. Contains 336421 sequences. (Running on oeis4.)