OFFSET
1,2
COMMENTS
The partitions into odd parts, encoded by their Heinz numbers. We define the Heinz number of a partition p = [p_1, p_2, ..., p_r] as Product(p_j-th prime, j=1...r) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). For example, for the partition [1, 1, 2, 4, 10] we get 2*2*3*7*29 = 2436. Example: 50 ( = 2*5*5) is in the sequence because it is the Heinz number of the partition [1, 3, 3]. - Emeric Deutsch, May 19 2015
From Peter Munn, Aug 11 2022: (Start)
Closed under multiplication.
Encodings, as defined in A206284, of even polynomials with nonnegative integer coefficients; so closed under application of A297845(.,.), which represents the multiplication of polynomials encoded this way.
(End)
For every positive integer m there exists a unique ordered pair of positive integers (j,k) such that m = a(j)*A066207(k). - Christopher Scussel, Aug 08 2023
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1001
EXAMPLE
20 is included because 20 = 2^2 * 5 = p(1)^2 * p(3) and 1 and 3 are both odd.
PROG
(PARI) { n=0; for (m=2, 10^9, f=factor(m); b=1; for(i=1, matsize(f)[1], if (primepi(f[i, 1])%2 == 0, b=0; break)); if (b, write("b066208.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 06 2010
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 16 2001
EXTENSIONS
Offset changed from 0 to 1 by Harry J. Smith, Feb 06 2010
a(61) and a(62) from Harry J. Smith, Feb 06 2010
1 prepended by Peter Munn, Aug 11 2022
STATUS
approved