A302040 Numbers k such that A078898(k) is a power of 2; an analog for A000961 based on factorization-kind of process involving the sieve of Eratosthenes (A083221).

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 29, 31, 32, 37, 41, 43, 45, 47, 49, 53, 55, 59, 61, 64, 67, 71, 73, 79, 83, 89, 91, 93, 97, 101, 103, 107, 109, 113, 115, 121, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 189, 191, 193, 197, 199, 203, 211, 223, 227, 229, 233, 235, 239, 241, 247, 251, 256, 257

Offset: 1

Author

Antti Karttunen, Apr 02 2018

Keywords

• nonn

Comments

Numbers k for which A302041(k) < 2, or equally, for which A302044(k) = 1.

Sequence A250245(A000961(k)) sorted into ascending order, or in other words, numbers k such that A250246(k) is a prime power (in A000961).

Numbers k such that all terms in iteration sequence k, A302042(k), A302042(A302042(k)), A302042(A302042(A302042(k))), ..., have an equal smallest prime factor (A020639) before the sequence settles to 1, in other words, that they all stay on the same row of A083221. This also forces the column position of each (A078898) to be a power of 2 (A000079).

Examples

			For k = 21 = 3*7, the smallest prime factor is 3. A302042(21) = 9, and A302042(9) = 3, both (9 and 3) which also have 3 as their smallest prime factor, and after that the sequence settles to 1, as A302042(3) = 1, thus 21 is included in this sequence.
For k = 27 = 3*3*3, the smallest prime factor is 3. However, A302042(27) = 7, thus 27 is not included in this sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6883
• Index entries for sequences generated by sieves

Crossrefs

Cf. A000961, A078898, A302036, A302041, A302044, A302053.

Cf. A000040, A000079, A001248 (subsequences).

Programs

PARI

for(n=1,257,if(2>A302041(n),print1(n,","))); \\ Other code as in A302041.