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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)

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

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Last modified June 17 19:57 EDT 2021. Contains 345085 sequences. (Running on oeis4.)