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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.
Sequence in context: A232241 A163836 A175085 * A099998 A360902 A365003
KEYWORD
nonn,easy
AUTHOR
Douglas Latimer, Apr 12 2012
STATUS
approved

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