A334104 Numbers m for which A329697(m) = 4.

43, 47, 49, 57, 59, 63, 67, 69, 71, 77, 79, 81, 86, 87, 91, 93, 94, 95, 98, 99, 105, 107, 109, 111, 114, 115, 117, 118, 121, 126, 131, 134, 135, 138, 142, 143, 145, 149, 151, 154, 155, 157, 158, 159, 162, 165, 167, 169, 172, 174, 175, 179, 181, 182, 183, 185, 186, 188, 190, 195, 196, 198, 210, 214, 218, 219, 222, 225

Offset: 1

Author

Antti Karttunen, Apr 14 2020

Keywords

• nonn

Comments

Squares of A334102 form a subsequence.

Among the first 12193 terms (terms < 2^31), there are terms with binary weights 2 - 16, except no terms with weight 13, 14 or 15. For example, 1025 is the first term with binary weight 2, and 65535 is the first term with binary weight 16.

Examples

			63 = 7*9 is a term as both 7 and 9 are terms of A334102.
65535 = 3*5*17*257 is a term as it is a product of four Fermat primes, thus in four steps all odd primes can be eliminated with p -> (p-1) map.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12193; all terms <= 2^31

Crossrefs

Row 4 of A334100.

Cf. A052126, A171462, A209229, A329697, A334101, A334102, A334103, A334105, A334106.

Cf. A334094 (primes present).

Programs

Mathematica

Position[Array[Length@NestWhileList[# - #/FactorInteger[#][[-1, 1]] &, #, # != 2^IntegerExponent[#, 2] &] - 1 &, 225], 4][[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]))));
isA334104(n) = (4==A329697(n));