A077618 Number of occurrences of n in A076734.
1, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 2, 0, 0, 1, 7, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 6, 1, 0, 1, 2, 1, 0, 1, 1, 0, 0, 1, 3, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 4, 1, 0, 1
Offset: 1
Keywords
Examples
For n=10, we have exactly two numbers k <= 10 such that A001222(k) = A001222(10) = 2, for which 10 is the least squarefree number >= k, namely 9 (= 3*3) and 10 (= 2*5), thus a(10) = 2. - _Antti Karttunen_, Oct 20 2017
Links
- Antti Karttunen, Table of n, a(n) for n = 1..30030
Programs
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Maple
N:= 200: # to get a(1)..a(N) M:= map(numtheory:-bigomega, [$1..N]): S:= map(numtheory:-issqrfree, [$1..N]): f:= proc(n) local m,k,t; if not S[n] then return 0 fi; m:= M[n]; t:= 1; for k from n-1 to 1 by -1 do if M[k] = m then if S[k] then return t else t:= t+1 fi; fi od; t end proc: map(f, [$1..N]); # Robert Israel, Oct 20 2017 -
Mathematica
Block[{nn = 120, s, t}, s = KeySelect[KeySort@ PositionIndex@ Array[Which[SquareFreeQ@ #1, #1, #3 < #1, #3, True, Block[{k = #1}, While[Nand[SquareFreeQ[k], PrimeOmega[k] == #2], k++]; k]] & @@ {#, PrimeOmega@ #, Times @@ Prime@ Range@ #} &, 2 nn], # < nn &]; t = ConstantArray[0, nn]; ReplacePart[t, Map[# -> Length@ Lookup[s, #] &, Keys@ s]]] (* Michael De Vlieger, Oct 20 2017 *) -
PARI
A077618(n) = { my(b = bigomega(n),s=1); if(1==n,n,if(!issquarefree(n),0,k=n-1; while(k > 1,if(bigomega(k)==b,if(issquarefree(k),return(s),s++)); k--; ); (s))); }; \\ Antti Karttunen, Oct 20 2017
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PARI
first(n) = {my(test = vector(n, i, [bigomega(i), i, issquarefree(i), 1]), biglist = vector(logint(n, 2) + 1)); forstep(i = n, 1, -1, if(test[i][3] == 0, test[i][4] = 0; if(biglist[test[i][1] + 1]!=0, test[biglist[test[i][1] + 1]][4]++) , biglist[test[i][1] + 1] = test[i][2])); vector(n, i, test[i][4])} \\ David A. Corneth, Oct 20 2017
Formula
a(A002110(n)) = A077622(n). - Antti Karttunen, Oct 20 2017, after Reinhard Zumkeller's comment in the latter sequence.
Extensions
Term a(10) corrected by Antti Karttunen, Oct 20 2017
Comments