

A278241


Least number with the same prime signature as the nth partition number: a(n) = A046523(A000041(n)).


6



1, 1, 2, 2, 2, 2, 2, 6, 6, 30, 30, 24, 6, 2, 24, 48, 30, 24, 30, 60, 30, 360, 30, 6, 180, 30, 420, 210, 60, 30, 60, 30, 60, 180, 30, 60, 2, 30, 60, 1680, 420, 210, 30, 240, 60, 30, 210, 420, 30, 60, 30, 60, 2310, 60, 2310, 420, 30, 30, 420, 4620, 30, 2310, 420, 30, 2310, 6, 6720, 6, 420, 30, 3360, 30, 30, 30, 2520, 120120, 6, 2, 420, 420, 1260, 6, 840, 30, 4620, 12
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OFFSET

0,3


COMMENTS

This sequence works as a "sentinel" for partition numbers by matching to any sequence that is obtained as f(A000041(n)), where f(n) is any function that depends only on the prime signature of n (see the index entry for "sequences computed from exponents in ..."). The last line in Crossrefs section lists such sequences that were present in the database as of Nov 11 2016.


LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10000 (terms 0..2527 from Antti Karttunen)
Index entries for sequences computed from exponents in factorization of n


FORMULA

a(n) = A046523(A000041(n)).


PROG

(PARI)
A046523(n) = my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ From Charles R Greathouse IV, Aug 17 2011
A278241(n) = A046523(numbpart(n));
for(n=0, 2310, write("b278241.txt", n, " ", A278241(n)));
(Scheme) (define (A278241 n) (A046523 (A000041 n)))


CROSSREFS

Cf. A000041, A046523, A278245, A278248.
Sequences that partition N into same or coarser equivalence classes: A085543, A085561, A087175.
Sequence in context: A104588 A157279 A214080 * A010671 A339164 A323443
Adjacent sequences: A278238 A278239 A278240 * A278242 A278243 A278244


KEYWORD

nonn


AUTHOR

Antti Karttunen, Nov 16 2016


STATUS

approved



