A334105 Numbers m for which A329697(m) = 5.

127, 129, 133, 139, 141, 147, 161, 163, 171, 173, 177, 189, 191, 197, 199, 201, 203, 207, 209, 211, 213, 215, 217, 223, 229, 231, 235, 237, 243, 245, 247, 253, 254, 258, 259, 261, 263, 266, 269, 271, 273, 277, 278, 279, 282, 285, 294, 295, 297, 299, 311, 315, 317, 319, 321, 322, 326, 327, 331, 333, 335, 341, 342, 345, 346, 349, 351

Offset: 1

Author

Antti Karttunen, Apr 14 2020

Keywords

• nonn

Examples

			127 = 63*2 + 1 is a term, as 127 is a prime and 63 is in A334104 as A329697(63) = 4.
2^32 -1 = 4294967295 = 3*5*17*257*65537 is a term as it is a product of five Fermat primes, thus in five steps all odd primes can be eliminated with p -> (p-1) map.
Likewise for 1442840405 = 5 * 17 * 257^3. (The first term with binary weight = 24).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..50071; all terms < 2^31

Crossrefs

Row 5 of A334100.

Cf. A052126, A171462, A209229, A329697, A334101, A334102, A334103, A334104, A334106.

Cf. A334095 (primes present).

Programs

Mathematica

Position[Array[Length@ NestWhileList[# - #/FactorInteger[#][[-1, 1]] &, #, # != 2^IntegerExponent[#, 2] &] - 1 &, 360], 5][[All, 1]] (* Michael De Vlieger, Apr 30 2020 *)

PARI

A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
isA334105(n) = (5==A329697(n));