login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A304465 If n is prime, set a(n) = 1. Otherwise, start with the multiset of prime factors of n, and given a multiset take the multiset of its multiplicities. Repeating this until a multiset of size 1 is reached, set a(n) to the unique element of this multiset. 42
0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 3, 1, 5, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 6, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 2, 3, 1, 2, 4, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(1) = 0 by convention.

a(n) depends only on prime signature of n (cf. A025487). - Antti Karttunen, Nov 08 2018

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(p^n) = n where p is any prime number.

a(product of n distinct primes) = n.

a(1) = 0; and for n > 1, if n = prime^k, a(n) = k, otherwise, if n is squarefree [i.e., A001221(n) = A001222(n)], a(n) = A001221(n), otherwise a(n) = a(A181819(n)). - Antti Karttunen, Nov 08 2018

EXAMPLE

Starting with the multiset of prime factors of 2520 we have {2,2,2,3,3,5,7} -> {1,1,2,3} -> {1,1,2} -> {1,2} -> {1,1} -> {2}, so a(2520) = 2.

MATHEMATICA

Table[Switch[n, 1, 0, _?PrimeQ, 1, _, NestWhile[Sort[Length/@Split[#]]&, Sort[Last/@FactorInteger[n]], Length[#]>1&]//First], {n, 100}]

PROG

(PARI)

A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));

A304465(n) = if(1==n, 0, my(t=isprimepower(n)); if(t, t, t=omega(n); if(bigomega(n)==t), t, A304465(A181819(n)))); \\ Antti Karttunen, Nov 08 2018

CROSSREFS

Cf. A000005, A001222, A001597, A005117, A007916, A055932, A056239, A112798, A181819, A182850, A182857, A275870, A296150, A303945, A304464.

Sequence in context: A077480 A327524 A059829 * A304687 A076558 A328195

Adjacent sequences:  A304462 A304463 A304464 * A304466 A304467 A304468

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 13 2018

EXTENSIONS

More terms from Antti Karttunen, Nov 08 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 06:15 EST 2019. Contains 329389 sequences. (Running on oeis4.)