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A278241 Least number with the same prime signature as the n-th 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 (list; graph; refs; listen; history; text; internal format)
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)
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
Sequences that partition N into same or coarser equivalence classes: A085543, A085561, A087175.
Sequence in context: A104588 A157279 A214080 * A010671 A339164 A323443
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 16 2016
STATUS
approved

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Last modified March 19 07:31 EDT 2024. Contains 370955 sequences. (Running on oeis4.)