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 A286708 Powerful numbers (A001694) that are not prime powers (A000961). 2
 36, 72, 100, 108, 144, 196, 200, 216, 225, 288, 324, 392, 400, 432, 441, 484, 500, 576, 648, 675, 676, 784, 800, 864, 900, 968, 972, 1000, 1089, 1125, 1152, 1156, 1225, 1296, 1323, 1352, 1372, 1444, 1521, 1568, 1600, 1728, 1764, 1800, 1936, 1944, 2000, 2025, 2116, 2304, 2312, 2500, 2592, 2601, 2700, 2704, 2744 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If a prime p divides a(n) then p^2 must also divide a(n) and number of distinct primes dividing a(n) > 1. Intersection of A001694 and A024619. LINKS Robert Israel, Table of n, a(n) for n = 1..5997 Eric Weisstein's World of Mathematics, Prime Power Eric Weisstein's World of Mathematics, Powerful Number EXAMPLE ------------------------------- | n | a(n) | prime            | |   |      | factorization    | |------------------------------ | 1 | 36   | {{2, 2}, {3, 2}} | | 2 | 72   | {{2, 3}, {3, 2}} | | 3 | 100  | {{2, 2}, {5, 2}} | | 4 | 108  | {{2, 2}, {3, 3}} | | 5 | 144  | {{2, 4}, {3, 2}} | | 6 | 196  | {{2, 2}, {7, 2}} | | 7 | 200  | {{2, 3}, {5, 2}} | | 8 | 216  | {{2, 3}, {3, 3}} | | 9 | 225  | {{3, 2}, {5, 2}} | ------------------------------- a(n) = p_1^e_1*p_2^e_2*... : {{p_1, e_1}, {p_2, e_2}, ...}. MAPLE N:= 10000: S:= {1}: P:= {1}: p:= 1: do   p:= nextprime(p);   if p^2 > N then break fi;   S:= map(s -> (s, seq(s*p^k, k = 2 .. floor(log[p](N/s)))), S);   P:= P union {seq(p^k, k=2..floor(log[p](N)))}: od: sort(convert(S minus P, list)); # Robert Israel, May 14 2017 MATHEMATICA Select[Range@2750, Min@FactorInteger[#][[All, 2]] > 1 && ! PrimePowerQ[#] &] CROSSREFS Cf. A000961, A001221, A001694, A024619, A131605. Sequence in context: A249726 A192026 A036785 * A114127 A322658 A224830 Adjacent sequences:  A286705 A286706 A286707 * A286709 A286710 A286711 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 13 2017 STATUS approved

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)