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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

Table of n, a(n) for n=1..34.

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);

CROSSREFS

Sequence in context: A090209 A283154 A157347 * A020408 A259424 A323330

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 June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)