This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332306 #10 May 07 2025 12:19:54 %S A332306 0,1,2,4,8,3,32,5,128,9,512,6,2048,33,10,65,32768,18,131072,12,34,513, %T A332306 2097152,7,8388608,2049,130,36,134217728,11,536870912,68,514,32769,40, %U A332306 19,34359738368,131073,2050,13,549755813888,35,2199023255552,516,136,2097153 %N A332306 a(n) is the least k such that A121663(k) = n. %C A332306 The binary representation of a(n) encodes the colexicographically earliest factorization of n into distinct factors greater than 1. %H A332306 Rémy Sigrist, <a href="/A332306/a332306.gp.txt">PARI program for A332306</a> %F A332306 a(n) = 2^(n-2) iff n is a prime number of the square of a prime number (A000430). %F A332306 a(n!) = 2^(n-1)-1 for any n > 0. %F A332306 a(p_1*...*p_k) = 2^(p_1-2)+...+2^(p_k-2) for distinct prime numbers p_1, ..., p_k. %e A332306 The first terms, alongside their binary representations and factorizations, are: %e A332306 n a(n) bin(a(n)) Factorization %e A332306 -- ------ ------------------ ------------- %e A332306 1 0 0 %e A332306 2 1 1 2 %e A332306 3 2 10 3 %e A332306 4 4 100 4 %e A332306 5 8 1000 5 %e A332306 6 3 11 2*3 %e A332306 7 32 100000 7 %e A332306 8 5 101 2*4 %e A332306 9 128 10000000 9 %e A332306 10 9 1001 2*5 %e A332306 11 512 1000000000 11 %e A332306 12 6 110 3*4 %e A332306 13 2048 100000000000 13 %e A332306 14 33 100001 2*7 %e A332306 15 10 1010 3*5 %e A332306 16 65 1000001 2*8 %e A332306 17 32768 1000000000000000 17 %e A332306 18 18 10010 3*6 %e A332306 19 131072 100000000000000000 19 %e A332306 20 12 1100 4*5 %o A332306 (PARI) See Links section. %Y A332306 Cf. A000430, A045778, A121663. %K A332306 nonn,base %O A332306 1,3 %A A332306 _Rémy Sigrist_, Feb 09 2020