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A062503
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Squarefree numbers squared.
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57
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1, 4, 9, 25, 36, 49, 100, 121, 169, 196, 225, 289, 361, 441, 484, 529, 676, 841, 900, 961, 1089, 1156, 1225, 1369, 1444, 1521, 1681, 1764, 1849, 2116, 2209, 2601, 2809, 3025, 3249, 3364, 3481, 3721, 3844, 4225, 4356, 4489, 4761, 4900, 5041, 5329, 5476
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Also, except for the initial term, numbers whose prime factors are squared. - Cino Hilliard, Jan 25 2006
Also cubefree numbers that are squares. - Gionata Neri, May 08 2016
All positive integers have a unique factorization into powers of squarefree numbers with distinct exponents that are powers of two. So every positive number is a product of at most one squarefree number (A005117), at most one square of a squarefree number (term of this sequence), at most one 4th power of a squarefree number (A113849), at most one 8th power of a squarefree number, and so on. - Peter Munn, Mar 12 2020
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LINKS
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FORMULA
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Numbers k such that Sum_{d|k} mu(d)*mu(k/d) = 1. - Benoit Cloitre, Mar 03 2004
For all k in the sequence, Omega(k) = 2*omega(k). - Wesley Ivan Hurt, Apr 30 2020
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MATHEMATICA
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Select[Range[100], SquareFreeQ]^2
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PROG
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(PARI) je=[]; for(n=1, 200, if(issquarefree(n), je=concat(je, n^2), )); je
(PARI) n=0; for (m=1, 10^5, if(issquarefree(m), write("b062503.txt", n++, " ", m^2); if (n==1000, break))) \\ Harry J. Smith, Aug 08 2009
(Haskell)
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CROSSREFS
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Characteristic function is A227291.
A329332 column 2 in ascending order.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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