The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A304465

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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.
(history; published version)

#18 by Susanna Cuyler at Thu Nov 08 21:13:25 EST 2018

STATUS

proposed

approved

#17 by Jon E. Schoenfield at Thu Nov 08 20:52:26 EST 2018

STATUS

editing

proposed

#16 by Jon E. Schoenfield at Thu Nov 08 20:52:22 EST 2018

LINKS

Antti Karttunen, <a href="/A304465/a304465.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

STATUS

proposed

editing

#15 by Antti Karttunen at Thu Nov 08 15:10:35 EST 2018

STATUS

editing

proposed

#14 by Antti Karttunen at Thu Nov 08 15:09:31 EST 2018

COMMENTS

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

LINKS

<a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

#13 by Antti Karttunen at Thu Nov 08 15:06:57 EST 2018

LINKS

Antti Karttunen, <a href="/A304465/a304465b304465.txt">TITLE FOR LINKTable of n, a(n) for n = 1..16384</a>

Antti Karttunen, <a href="/A304465/a304465.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

#12 by Antti Karttunen at Thu Nov 08 15:04:49 EST 2018

LINKS

Antti Karttunen, <a href="/A304465/a304465.txt">TITLE FOR LINK</a>

#11 by Antti Karttunen at Thu Nov 08 14:59:26 EST 2018

DATA

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

FORMULA

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

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

EXTENSIONS

More terms from Antti Karttunen, Nov 08 2018

STATUS

approved

editing

#10 by Susanna Cuyler at Mon May 14 20:23:39 EDT 2018

STATUS

proposed

approved

#9 by Gus Wiseman at Sun May 13 12:40:23 EDT 2018

STATUS

editing

proposed