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 A164283 Number of ways to write n as the root-mean-square (RMS) of a set of distinct positive integers. 4
 1, 1, 1, 1, 3, 9, 19, 79, 225, 693, 1901, 5597, 17641, 57503, 195431, 647139, 2182987, 7344451, 25057681, 85742999, 295284367, 1028155825, 3596134963, 12659796475, 44696280143, 158226554179, 562623263251, 2006471222195, 7182910999719, 25795458946677, 92875047372825, 335362896810137 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Eric Weisstein's World of Math, Root-Mean-Square EXAMPLE a(6) = 9, because 6 is the RMS of 9 sets of distinct positive integers: 6 = RMS(6) = RMS(1,3,5,8,9) = RMS(3,4,5,7,9) = RMS(1,2,4,5,7,11) = RMS(1,3,5,6,8,9) = RMS(3,4,5,6,7,9) = RMS(1,2,3,5,7,8,10) = RMS(1,2,4,5,6,7,11) = RMS(1,2,3,5,6,7,8,10). MAPLE sns:= proc(i) option remember; `if`(i=1, 1, sns(i-1) +i^2) end: b:= proc(n, i, t) if n<0 or i nl  = 0      | yy < nl  = f ks (l + 1) (nl + nn) yy + f ks l nl xx      | otherwise = if w == n then 1 else 0      where w = if r == 0 then a000196 m else 0            (m, r) = divMod yy l            yy = xx + k * k    nn = n ^ 2 -- Reinhard Zumkeller, Feb 13 2013 CROSSREFS Cf. A163974, A066572, A066571, A072701. Cf. A000196, A211868. Sequence in context: A130586 A147146 A146066 * A178963 A033315 A200612 Adjacent sequences:  A164280 A164281 A164282 * A164284 A164285 A164286 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 12 2009 STATUS approved

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Last modified August 1 13:00 EDT 2021. Contains 346391 sequences. (Running on oeis4.)