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 A255356 Composite squarefree numbers that are multiples of the root mean square of their prime factors. 0
 1547, 2737, 4305, 6545, 13585, 39997, 52633, 57505, 65773, 77441, 93023, 115855, 202895, 214415, 285649, 308865, 315905, 352495, 352735, 443555, 449497, 510229, 510655, 523439, 611295, 627095, 650845, 700321, 722545, 881705, 936845, 1088255, 1103795, 1392047 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Eric Weisstein's World of Mathematics, Root-Mean-Square. EXAMPLE Prime factors of 1547 are 7, 13, 17. Their root mean square is sqrt((7^2 + 13^2 + 17^2) / 3) = sqrt((49 + 169 + 289) / 3) = sqrt(507 / 3) = sqrt(169) = 13 and 1547 / 13 = 119. Prime factors of 2737 are 7, 17, 23. Their root mean square is sqrt((7^2 + 17^2 + 23^2) / 3) = sqrt((49 + 289 + 529) / 3) = sqrt(867 / 3) = sqrt(289) = 17 and 2737 / 17 = 161. MAPLE with(numtheory); P:=proc(q) local a, b, c, k, n; for n from 2 to q do if not isprime(n) and issqrfree(n) then a:=ifactors(n)[2]; c:=add(a[k][2], k=1..nops(a)); b:=sqrt(add(a[k][2]*a[k][1]^2, k=1..nops(a))/c); if type(n/b, integer) then print(n); fi; fi; od; end: P(10^9); MATHEMATICA q[n_] := Module[{f = FactorInteger[n]}, Length[f] > 1 && AllTrue[f[[;; , 2]], # == 1 &] && Divisible[n, RootMeanSquare[f[[;; , 1]]]]]; Select[Range[10^5], q] (* Amiram Eldar, Feb 24 2021 *) CROSSREFS Cf. A120944. Sequence in context: A090209 A283154 A157347 * A336221 A020408 A259424 Adjacent sequences:  A255353 A255354 A255355 * A255357 A255358 A255359 KEYWORD nonn AUTHOR Paolo P. Lava, Feb 23 2015 STATUS approved

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Last modified January 19 09:16 EST 2022. Contains 350464 sequences. (Running on oeis4.)