A097273 Least integer with each "mod 2 prime signature".

1, 2, 3, 4, 6, 8, 9, 12, 15, 16, 18, 24, 27, 30, 32, 36, 45, 48, 54, 60, 64, 72, 81, 90, 96, 105, 108, 120, 128, 135, 144, 162, 180, 192, 210, 216, 225, 240, 243, 256, 270, 288, 315, 324, 360, 384, 405, 420, 432, 450, 480, 486, 512, 540, 576, 630, 648, 675, 720

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

Cf. A097272, A097274, A097275.

Cf. A025487, A070826, A147516.

Sequence in context: A231404 A364291 A316860 * A006446 A261342 A002348

Adjacent sequences: A097270 A097271 A097272 * A097274 A097275 A097276

Keyword

nonn

Author

Ray Chandler, Aug 22 2004

Extensions

Offset corrected by Amiram Eldar, Jul 23 2024

Status

approved