A309263 Terms of A140110 that are not divisible by 6.

1, 2, 4, 8, 16, 20, 32, 64, 100, 128, 256, 272, 500, 512, 1024, 2048, 2500, 4096, 4624, 8192, 10100, 12500, 16384, 32768, 62500, 65536, 65792, 78608, 131072, 262144, 312500, 524288, 1020100, 1048576, 1336336, 1562500, 2097152, 4194304, 7812500, 8388608

Offset: 1

Author

J. Lowell, Jul 19 2019

Keywords

• nonn

Comments

Includes all powers of 2.

Conjecture: The sequence includes all numbers of the form 4*5^n.

The number 10100 is a counterexample for: (a) Prime factorizations of numbers of this sequence will always have only 2's and Fermat primes. (b) No number in this sequence is divisible by more than one distinct odd prime.

Examples

			20 is in this sequence because it is in A140110 and is not divisible by 6.
24, which is in A140110, is not in this sequence because it is divisible by 6.
		

Crossrefs

Cf. A140110, A000079, A005054.

Programs

PARI

isok(n) = {if(n%6 == 0, return(0)); my(d = divisors(n)); for (k=1, #d - 1, r = d[k+1]/d[k]; if(numerator(r) != denominator(r) + 1, return(0)); ); return(1); } \\ Jinyuan Wang, Aug 03 2019