A274718 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A274718

Set x = n. Then a(n) is the number of iterations of successive applications of the map x = A001414(x) that leave x composite, or a(n) = -1 if x always remains composite.

-1, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 0, 2, 1, 3, 2, 0, 0, 1, 0, 1, 3, 0, 1, 1, 0, 2, 3, 0, 0, 1, 0, 3, 0, 2, 0, 0, 3, 1, 3, 0, 0, 0, 3, 0, 1, 0, 0, 1, 0, 4, 0, 1, 3, 3, 0, 2, 4, 3, 0, 1, 0, 4, 0, 0, 3, 3, 0, 0, 1, 0, 0, 3, 1, 1, 2, 0, 0, 0, 3, 3, 1, 4, 3, 0, 0, 3, 0, 3, 0, 1, 0, 0, 3

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,14

COMMENTS

a(1) and a(4) are the only terms with a value of -1.

a(n) = 0 iff n is a term of A100118.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

EXAMPLE

For n = 26: A001414(26) = 15, A001414(15) = 8, A001414(8) = 6 and A001414(6) = 5. 5 is prime and so 26 remains composite through 3 iterations of the map given in the definition, therefore a(26) = 3.

MATHEMATICA

lim = 10^4; Table[Length@ NestWhileList[If[# == 1, 0, Total@ Flatten[Table[#1, {#2}] & @@@ FactorInteger@ #]] &, n, ! PrimeQ@ # &, 1, lim] - 2 /. {-1 -> 0, lim - 1 -> -1}, {n, 86}] (* Michael De Vlieger, Jul 03 2016 *)

PROG

(PARI) sopfr(n) = my(f=factor(n)); sum(i=1, #f[, 1], f[i, 1]*f[i, 2]) /* after Charles R Greathouse IV in A050703 */

a(n) = my(i=0, s=sopfr(n)); while(1, if(ispseudoprime(s), return(i)); if(s==sopfr(s), return(-1)); s=sopfr(s); i++)

CROSSREFS

Cf. A001414, A100118.

Sequence in context: A133625 A373926 A176154 * A028930 A112792 A138319

Adjacent sequences: A274715 A274716 A274717 * A274719 A274720 A274721

KEYWORD

sign

AUTHOR

Felix Fröhlich, Jul 03 2016

EXTENSIONS

More terms from Antti Karttunen, Mar 07 2018

STATUS

approved