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 A008479 Number of numbers <= n with same prime factors as n. 16
 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 4, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 6, 2, 4, 1, 2, 1, 7, 1, 3, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 3, 2, 1, 1, 1, 5, 4, 1, 1, 2, 1, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS For n > 1, a(n) gives the (one-based) index of the row where n is located in arrays A284311 and A285321 or respectively, index of the column where n is in A284457. A285329 gives the other index. - Antti Karttunen, Apr 17 2017 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 P. Erdős, T. Motzkin, Problem 5735, Amer. Math. Monthly, 78 (1971), 680-681. (Incorrect solution!) H. N. Shapiro, Problem 5735, Amer. Math. Monthly, 97 (1990), 937. FORMULA a(n) = Sum_{k=1..n} (floor(n^k/k)-floor((n^k-1)/k))*(floor(k^n/n)-floor((k^n-1)/n)). - Anthony Browne, May 20 2016 If A008683(n) <> 0 [when n is squarefree, A005117], a(n) = 1, otherwise a(n) = 1+a(A285328(n)). - Antti Karttunen, Apr 17 2017 MAPLE N:= 100: # to get a(1)..a(N) V:= Vector(N): V[1]:= 1: for n from 2 to N do   if V[n] = 0 then    S:= {n};    for p in numtheory:-factorset(n) do      S := S union {seq(seq(s*p^k, k=1..floor(log[p](N/s))), s=S)};    od:    S:= sort(convert(S, list));    for k from 1 to nops(S) do V[S[k]]:= k od: fi od: convert(V, list); # Robert Israel, May 20 2016 MATHEMATICA PkTbl=Prepend[ Array[ Times @@ First[ Transpose[ FactorInteger[ # ] ] ]&, 100, 2 ], 1 ]; 1+Array[ Count[ Take[ PkTbl, #-1 ], PkTbl[ [ # ] ] ]&, Length[ PkTbl ] ] Count[#, k_ /; k == Last@ #] & /@ Function[s, Take[s, #] & /@ Range@ Length@ s]@ Array[Map[First, FactorInteger@ #] &, 120] (* or *) Table[Sum[(Floor[n^k/k] - Floor[(n^k - 1)/k]) (Floor[k^n/n] - Floor[(k^n - 1)/n]), {k, n}], {n, 120}] (* Michael De Vlieger, May 20 2016 *) PROG (Scheme) (define (A008479 n) (if (not (zero? (A008683 n))) 1 (+ 1 (A008479 (A285328 n))))) ;; Antti Karttunen, Apr 17 2017 (PARI) a(n)=my(f=factor(n)[, 1], s); forvec(v=vector(#f, i, [1, logint(n, f[i])]), if(prod(i=1, #f, f[i]^v[i])<=n, s++)); s \\ Charles R Greathouse IV, Oct 19 2017 CROSSREFS Cf. A005117 (positions of ones), A005361, A007947, A008683, A284311, A284457, A285321, A285328, A285329. Sequence in context: A303915 A322885 A292582 * A227350 A107345 A000688 Adjacent sequences:  A008476 A008477 A008478 * A008480 A008481 A008482 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)