A277886 If n is squarefree, a(n) = n, else a(n) = A000040(1+A277885(n)) * (n/(A249739(n)^2)).

1, 2, 3, 3, 5, 6, 7, 6, 5, 10, 11, 9, 13, 14, 15, 12, 17, 10, 19, 15, 21, 22, 23, 18, 7, 26, 15, 21, 29, 30, 31, 24, 33, 34, 35, 27, 37, 38, 39, 30, 41, 42, 43, 33, 25, 46, 47, 36, 11, 14, 51, 39, 53, 30, 55, 42, 57, 58, 59, 45, 61, 62, 35, 48, 65, 66, 67, 51, 69, 70, 71, 54, 73, 74, 21, 57, 77, 78, 79, 60, 45

Offset

1,2

Comments

If n has non-unitary prime divisors, then divide it by the square of the smallest of them and multiply by a single instance of the next larger prime.

This differs from related A097246 for the first time at n=16. For both sequences A097248 gives the eventual stable points reached when starting iterating from n.

Links

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

Formula

If A277885(n) = 0 [when n is squarefree], then a(n) = n, otherwise a(n) = A000040(1+A277885(n)) * (n/(A249739(n)^2)).

Other identities. For all n >= 1:

A048675(a(n)) = A048675(n).

Example

For n = 12 = 2*2*3, the smallest non-unitary prime divisor (and in this case the only one) is 2, thus we divide with 2^2 and multiply with the next larger prime 3, to get ((2^2 * 3)/(2^2))*3 = 3*3, thus a(12) = 9.
For n = 16 = 2^4, we divide two instances of 2 out and multiply by a single instance of 3 to get 2*2*3 = 12.

Mathematica

Table[If[SquareFreeQ@ n, n, Prime[1 + PrimePi@ Min[Select[FactorInteger[n][[All, 1]], ! CoprimeQ[#, n/#] &] /. {} -> 0]] (n/If[SquareFreeQ@ n, 1, p = 2; While[! Divisible[n, p^2], p = NextPrime@ p]; p]^2)], {n, 81}] (* Michael De Vlieger, Nov 15 2016 *)

Prog

(Scheme) (define (A277886 n) (if (zero? (A277885 n)) n (* (A000040 (+ 1 (A277885 n))) (/ n (expt (A249739 n) 2)))))

Crossrefs

Cf. A000040, A048675, A097246, A097248, A249739, A277885, A277887, A277888, A277896.

Sequence in context: A097248 A097247 A097246 * A359588 A337868 A063659

Adjacent sequences: A277883 A277884 A277885 * A277887 A277888 A277889

Keyword

nonn

Author

Antti Karttunen, Nov 08 2016

Status

approved