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A252462 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. 7
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 (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.

LINKS

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

FORMULA

a(1) = 1; for n>1: a(n) = A008578(A061395(n)) * A052126(n). [Compare to the similar formula given for A064989.]

a(n) = A008578(1 + A252735(n)) * A052126(n).

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.]

MATHEMATICA

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];

Array[a, n]]; a252462[84] (* Michael De Vlieger, Dec 21 2014 *)

PROG

(Scheme) (define (A252462 n) (if (= 1 n) n  (* (A008578 (A061395 n)) (A052126 n))))

CROSSREFS

Variant: A252461.

Cf. A001222, A008578, A052126, A061395, A056239, A064989, A209229, A252735.

Sequence in context: A293428 A281487 A224401 * A094457 A275495 A022820

Adjacent sequences:  A252459 A252460 A252461 * A252463 A252464 A252465

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 20 2014

STATUS

approved

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Last modified November 15 18:59 EST 2019. Contains 329149 sequences. (Running on oeis4.)