A302053 Squares (A000290) analog for nonstandard factorization process based on the sieve of Eratosthenes (A083221).

0, 1, 4, 9, 16, 25, 36, 45, 49, 64, 100, 105, 115, 121, 144, 169, 180, 189, 196, 203, 256, 265, 289, 297, 341, 361, 400, 420, 429, 460, 469, 475, 481, 484, 529, 537, 576, 585, 676, 697, 720, 745, 756, 765, 784, 803, 812, 817, 833, 841, 961, 1024, 1027, 1060, 1075, 1081, 1156, 1188, 1197, 1257, 1309, 1345, 1364, 1369, 1377, 1411, 1444

Offset: 0

Author

Antti Karttunen, Mar 31 2018

Keywords

• nonn

Comments

Indexing starts with zero, with a(0) = 0, to match with the indexing of A000290.

After initial zero, gives the positions of odd terms in A302051.

After initial zero, contains values obtained with A250245(n^2) sorted into ascending order, or in other words, numbers n such that A250246(n) is a square (in A000290).

Numbers n such that for all terms in iteration sequence n, A302044(n), A302044(A302044(n)), A302044(A302044(A302044(n))), ..., applying A302045(n) gives an even number before the sequence settles to 1.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..3283
• Index entries for sequences generated by sieves

Crossrefs

Cf. A000290, A250245, A302051, A302040, A302044, A302045, A302052 (characteristic function).

Cf. A000302, A001248 (subsequences).

Programs

PARI

for(n=0,4096,if(1==A302052(n),print1(n,",")));