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

1,2

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).

Links

Antti Karttunen, Table of n, a(n) for n = 1..6883

Index entries for sequences generated by sieves

Example

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.

Prog

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

Crossrefs

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

Cf. A000040, A000079, A001248 (subsequences).

Sequence in context: A328867 A326536 A322902 * A302036 A357864 A331912

Adjacent sequences: A302037 A302038 A302039 * A302041 A302042 A302043

Keyword

nonn

Author

Antti Karttunen, Apr 02 2018

Status

approved