The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182120 Numbers for which the canonical prime factorization contains only exponents which are congruent to 2 modulo 3. 3
 1, 4, 9, 25, 32, 36, 49, 100, 121, 169, 196, 225, 243, 256, 288, 289, 361, 441, 484, 529, 676, 800, 841, 900, 961, 972, 1089, 1156, 1225, 1369, 1444, 1521, 1568, 1681, 1764, 1849, 2048, 2116, 2209, 2304, 2601, 2809, 3025, 3125, 3249, 3364, 3481, 3721, 3844 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS By convention 1 is included as the first term. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Douglas Latimer) FORMULA Sum_{n>=1} 1/a(n) = zeta(3) * Product_{p prime} (1 + 1/p^2 - 1/p^3) = 1.56984817927051410948... . - Amiram Eldar, Oct 21 2023 EXAMPLE 100 is included, as its canonical prime factorization (2^2)*(5^2) contains only exponents which are congruent to 2 modulo 3. MATHEMATICA Join[{1}, Select[Range[5000], Union[Mod[Transpose[FactorInteger[#]][[2]], 3]] == {2}&]] (* Harvey P. Dale, Aug 18 2014 *) PROG (PARI) {plnt=1; k=1; print1(k, ", "); plnt++; mxind=76 ; mxind++ ; for(k=2, 2*10^6, M=factor(k); passes=1; sz = matsize(M)[1]; for(k=1, sz, if( M[k, 2] % 3 != 2, passes=0)); if( passes == 1 , print1(k, ", "); plnt++) ; if(mxind == plnt, break() ))} (PARI) is(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 2]%3 != 2, return(0))); 1; } \\ Amiram Eldar, Oct 21 2023 CROSSREFS A062503 is a subsequence. Subsequence of A001694. Cf. A002117, A366762. Sequence in context: A232241 A163836 A175085 * A099998 A360902 A365003 Adjacent sequences: A182117 A182118 A182119 * A182121 A182122 A182123 KEYWORD nonn,easy AUTHOR Douglas Latimer, Apr 12 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 23 19:56 EDT 2024. Contains 371916 sequences. (Running on oeis4.)