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A252461 Shift one instance of the smallest prime one step towards smaller primes: a(1) = 1, a(2n) = n, and for odd numbers > 1: a(n) = (n / prime(s)) * prime(s-1), where s = A055396(n), index of the smallest prime dividing n. 6
1, 1, 2, 2, 3, 3, 5, 4, 6, 5, 7, 6, 11, 7, 10, 8, 13, 9, 17, 10, 14, 11, 19, 12, 15, 13, 18, 14, 23, 15, 29, 16, 22, 17, 21, 18, 31, 19, 26, 20, 37, 21, 41, 22, 30, 23, 43, 24, 35, 25, 34, 26, 47, 27, 33, 28, 38, 29, 53, 30, 59, 31, 42, 32, 39, 33, 61, 34, 46, 35, 67, 36, 71, 37, 50, 38, 55, 39, 73, 40, 54, 41, 79, 42 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Iterating from any n as a(n), a(a(n)), a(a(a(n))), etc. reaches 1 after A056239(n) iterations.

Even bisection gives the natural numbers A000027, the odd bisection from the third term onward is A129128: 2, 3, 5, 6, 7, 11, 10, ...

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(1) = 1; for n>1: a(n) = A008578(A055396(n)) * A032742(n). [Compare to the similar formula of A064989.]

Other identities. For all n >= 1:

a(2n) = n.

If n is odd, A001222(a(n)) = A001222(n).

If n is even, A001222(a(n)) = A001222(n) - 1.

MATHEMATICA

a252461[n_Integer] := Block[{a008578, a032742, a055396, a},

  a008578[x_] := If[x == 1, 1, Prime[x - 1]];

  a032742[x_] := If[x == 1, 1, Divisors[x][[-2]]];

  a055396[x_] := PrimePi[FactorInteger[x][[1]][[1]]];

  a[1] = 1;

  a[x_] := a008578[a055396[x]]*a032742[x];

Array[a, n]]; a252461[84] (* Michael De Vlieger, Dec 21 2014 *)

PROG

(Scheme) (define (A252461 n) (if (= 1 n) n (* (A008578 (A055396 n)) (A032742 n))))

CROSSREFS

Variants: A252462, A252463.

Bisections: A000027, A129128.

Cf. A001222, A008578, A032742, A055396, A056239, A064989.

Sequence in context: A007150 A213634 A300271 * A323608 A122352 A248519

Adjacent sequences:  A252458 A252459 A252460 * A252462 A252463 A252464

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 20 2014

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)