OFFSET
1,2
COMMENTS
For n = 2^e_0 * p_1^e_1 * ... * p_n^e_n where p_i is odd prime and e_1 >= e_2 >= ... >= e_n, define "mod 2 prime signature" to be ordered prime exponents (e_0,e_1,...,e_n).
Least integer with a given mod 2 prime signature is obtained by replacing p_1 with 3, p_2 with 5,..., p_n with n-th odd prime.
A097272 sorted and duplicates removed.
Numbers k such that A097272(k) = k.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{n>=1} 1/a(n) = 2 * Product_{n>=2} 1/(1 - 1/A070826(n)) = 3.2482341898... . - Amiram Eldar, Jul 23 2024
MATHEMATICA
lpsQ[n_] := n==1 || (Max@ Differences[(f = FactorInteger[n])[[;; , 2]]] < 1 && f[[-1, 1]] == Prime[Length[f] + 1]); Select[Range[1000], lpsQ[# / 2^IntegerExponent[#, 2]] &] (* Amiram Eldar, Jul 23 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ray Chandler, Aug 22 2004
EXTENSIONS
Offset corrected by Amiram Eldar, Jul 23 2024
STATUS
approved