A385531
Numbers x such that there exist three integers 00 such that sigma(x)^2 = sigma(y)^2 = sigma(z)^2 = x^2 + y^2 + z^2 + t^2.
4, 6, 28, 45, 48, 60, 156, 204, 208, 360, 496, 1170, 2016, 2520, 2925, 3480, 4796, 5532, 5733, 7152, 7605, 8128, 9680, 11050, 12402, 15776, 33468, 36720, 37064, 38408, 43584, 50960, 55216, 63708, 70364, 83772, 92280, 106700, 114840, 116288, 149400, 163800, 166617, 167580
Offset: 1
Examples
(3480, 3672, 4296, 8520) is such a quadruple because sigma(3480)^2 = sigma(3672)^2 = sigma(4296)^2 = 3480^2 + 3672^2 + 4296^2 + 8520^2.
Links
- David A. Corneth, Table of n, a(n) for n = 1..97
- Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).
- David A. Corneth, PARI program
- S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.
Programs
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PARI
isok(x) = my(s=sigma(x), vi=select(t->(t>=x), invsigma(s))); for (i=1, #vi, for (j=1, #vi, for (k=1, #vi, if ((i==1) || (j==1) || (k==1), my(ss = s^2 - vi[i]^2 - vi[j]^2 - vi[k]^2); if (ss && issquare(ss), return(1)););););); \\ Michel Marcus, Jul 09 2025
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PARI
\\ See Corneth link
Extensions
Some missing terms added by Michel Marcus, Jul 09 2025
More terms from David A. Corneth, Jul 09 2025
Comments