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

1,2

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.

Links

Table of n, a(n) for n=1..40.

Example

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.

Prog

(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

Crossrefs

Cf. A140110, A000079, A005054.

Sequence in context: A093107 A125508 A067945 * A166156 A089473 A118021

Adjacent sequences: A309260 A309261 A309262 * A309264 A309265 A309266

Keyword

nonn

Author

J. Lowell, Jul 19 2019

Status

approved