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A046668 Numbers n such that partition function p(n) divides n!. 1
1, 2, 3, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 24, 28, 32, 33, 39 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The symmetric group has p(n) conjugacy classes and order n! The sequence arose in a search for groups G which satisfy Pr(G) = k(G)/|G| = 1/t, for integer t, where G has k(G) conjugacy classes.

The next term, if it exists, is > 30000. - Emeric Deutsch, Feb 26 2005

The next term, if it exists, is > 350000. - David A. Corneth, Jul 04 2018

The next term, if it exists, is > 2000000. - Vaclav Kotesovec, Jul 06 2018

REFERENCES

Commutativity and Generalizations in Finite Groups; Aine NiShe, Ph.D. thesis in preparation.

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

1 is a term, since p(1) = 1 and 1 divides 1 = 1!.

7 is a term because p(7) = 15 and 15 divides 7! = 5040.

MAPLE

with(combinat): p:=proc(n) if type(n!/numbpart(n), integer) then n fi end; seq(p(n), n=1..300); # Emeric Deutsch

MATHEMATICA

Do[ If[ Mod[n!, PartitionsP[n]] == 0, Print[n]], {n, 10000}] (* Robert G. Wilson v, Nov 23 2004 *)

Select[Range[40], Divisible[#!, PartitionsP[#]]&] (* Harvey P. Dale, Jan 30 2015 *)

PROG

(MAGMA) [ n : n in [1..40] | Factorial(n) mod NumberOfPartitions(n) eq 0 ]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

(PARI) val(n, p) = my(r=0); while(n, r+=n\=p); r

is(n) = qp = numbpart(n); forprime(p = 2, n, if(val(n, p) < valuation(qp, p), return(0)); qp/=p^valuation(qp, p)); qp==1 \\ David A. Corneth, Jul 04 2018

CROSSREFS

Cf. A000041, A000142, A316530.

Sequence in context: A114056 A168222 A140221 * A047533 A060525 A152863

Adjacent sequences:  A046665 A046666 A046667 * A046669 A046670 A046671

KEYWORD

nonn,nice,more

AUTHOR

Des MacHale

STATUS

approved

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Last modified August 14 04:36 EDT 2018. Contains 313748 sequences. (Running on oeis4.)