

A088902


Numbers n such that n = product (p_k)^(c_k) and set of its (c_k k's)'s is a selfconjugate partition, where p_k is kth prime and c_k > 0.


10



1, 2, 6, 9, 20, 30, 56, 75, 84, 125, 176, 210, 264, 350, 416, 441, 624, 660, 735, 1088, 1100, 1386, 1560, 1632, 1715, 2310, 2401, 2432, 2600, 3267, 3276, 3648, 4080, 5390, 5445, 5460, 5888, 6800, 7546, 7722, 8568, 8832, 9120, 12705, 12740, 12870, 13689
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OFFSET

1,2


COMMENTS

The Heinz numbers of the selfconjugate partitions. We define the Heinz number of a partition p = [p_1, p_2, ..., p_r] to be Product(p_jth prime, j=1...r) (a concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). For example, for the partition [1, 1, 1, 4] we get 2*2*2*7 = 56. It is in the sequence since [1,1,1,4] is selfconjugate.  Emeric Deutsch, Jun 05 2015


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..400


EXAMPLE

20 is in the sequence because 20 = 2^2 * 5^1 = (p_1)^2 *(p_3)^1, (two 1's, one 3's) = (1,1,3) is a selfconjugate partition of 5.


MAPLE

with(numtheory): c := proc (n) local B, C: B := proc (n) local pf: pf := op(2, ifactors(n)): [seq(seq(pi(op(1, op(i, pf))), j = 1 .. op(2, op(i, pf))), i = 1 .. nops(pf))] end proc: C := proc (P) local a: a := proc (j) local c, i: c := 0: for i to nops(P) do if j <= P[i] then c := c+1 else end if end do: c end proc: [seq(a(k), k = 1 .. max(P))] end proc: mul(ithprime(C(B(n))[q]), q = 1 .. nops(C(B(n)))) end proc: SC := {}: for i to 14000 do if c(i) = i then SC := `union`(SC, {i}) else end if end do: SC; # Emeric Deutsch, May 09 2015


MATHEMATICA

Select[Range[14000], Function[n, n == If[n == 1, 1, Module[{l = #, m = 0}, Times @@ Power @@@ Table[l = m; l = DeleteCases[l, 0]; {Prime@ Length@ l, m = Min@ l}, Length@ Union@ l]] &@ Catenate[ConstantArray[PrimePi@ #1, #2] & @@@ FactorInteger@ n]]]] (* Michael De Vlieger, Aug 27 2016, after JungHwan Min at A122111 *)


PROG

(Scheme, with Antti Karttunen's Intseqlibrary)
(define A088902 (FIXEDPOINTS 1 1 A122111))


CROSSREFS

Fixed points of A122111.
Cf. A056239, A000700, A242422, A215366.
A002110 (primorial numbers) is a subsequence.
After a(1) and a(2), a subsequence of A241913.
Sequence in context: A093840 A129233 A106529 * A265016 A279897 A095967
Adjacent sequences: A088899 A088900 A088901 * A088903 A088904 A088905


KEYWORD

easy,nonn


AUTHOR

Naohiro Nomoto, Nov 28 2003


EXTENSIONS

More terms from David Wasserman, Aug 26 2005


STATUS

approved



