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A319688
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Sum of digits when n is represented in phitorial (A001088) base.
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1
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0, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6
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OFFSET
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0,4
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LINKS
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FORMULA
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Starting from i=3, compute the remainder when n is divided by phi(i), and then continue iterating with n -> floor(n/phi(i)), and i -> i+1, until n is zero. a(n) is the sum of remainders encountered in process.
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EXAMPLE
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For n = 9, its phitorial representation is "102" as 9 = 1*A001088(2) + 0*A001088(3) + 2*A001088(4) = 1*1 + 0*2 + 2*4. Thus a(9) = 1+0+2 = 3.
For n = 577, its phitorial representation is "300001" as 577 = 1*A001088(2) + 3*A001088(7) = 1*1 + 3*192, thus a(577) = 4.
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MATHEMATICA
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With[{max = 7}, bases = EulerPhi[Range[max, 1, -1]]; nmax = Times @@ bases - 1; a[n_] := Plus @@ IntegerDigits[n, MixedRadix[bases]]; Array[a, nmax, 0]] (* Amiram Eldar, Jul 29 2023 *)
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PROG
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(PARI) A319688(n) = { my(s=0, i=3, d, b); while(n, b = eulerphi(i); d = (n%b); s += d; n = (n-d)/b; i++); (s); };
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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