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.

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

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