A278241 Least number with the same prime signature as the n-th partition number: a(n) = A046523(A000041(n)).

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

Offset: 0

Author

Antti Karttunen, Nov 16 2016

Keywords

• nonn

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

Crossrefs

Cf. A000041, A046523, A278245, A278248.

Sequences that partition N into same or coarser equivalence classes: A085543, A085561, A087175.

Programs

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)))

Formula

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