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A252462
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Shift one instance of the largest prime one step towards smaller primes: a(1) = 1, a(2^n) = 2^(n-1), and for other numbers: a(n) = (n / prime(g)) * prime(g-1), where g = A061395(n), index of the greatest prime dividing n.
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7
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1, 1, 2, 2, 3, 4, 5, 4, 6, 6, 7, 8, 11, 10, 9, 8, 13, 12, 17, 12, 15, 14, 19, 16, 15, 22, 18, 20, 23, 18, 29, 16, 21, 26, 25, 24, 31, 34, 33, 24, 37, 30, 41, 28, 27, 38, 43, 32, 35, 30, 39, 44, 47, 36, 35, 40, 51, 46, 53, 36, 59, 58, 45, 32, 55, 42, 61, 52, 57, 50, 67, 48, 71, 62, 45, 68, 49, 66, 73, 48, 54, 74, 79, 60
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OFFSET
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1,3
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COMMENTS
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Iterating from any n as a(n), a(a(n)), a(a(a(n))), etc. reaches 1 after A056239(n) iterations.
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LINKS
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FORMULA
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Other identities. For all n >= 1:
a(2^n) = 2^(n-1).
For n >= 2, A001222(a(n)) = A001222(n) - A209229(n). [Number of prime divisors decreases only when n is a power of 2 larger than 1.]
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MATHEMATICA
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a252462[n_Integer] := Block[{a008578, a052126, a061395, a},
a008578[x_] := If[x == 1, 1, Prime[x - 1]];
a052126[x_] := If[x == 1, 1, x/FactorInteger[x][[-1]][[1]]];
a061395[x_] := PrimePi[FactorInteger[x][[-1]][[1]]];
a[1] = 1;
a[x_] := a008578[a061395[x]]*a052126[x];
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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