This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
A382506(16) = 465, 465 + sigma(16) = 496, which is perfect.
sigma(6) = 12, the nearest perfect number is 6, thus a(6) = 12 - 6 = 6. sigma(26) = 42, the nearest perfect number is 28, thus a(26) = 42 - 28 = 14.
isA000396 := proc(n::integer) if n < 6 then false ; elif numtheory[sigma](n) = 2*n then true; else false; end if; end proc: A382483 := proc(n) local k ; for k from 0 do if isA000396(numtheory[sigma](n)-k) or isA000396(numtheory[sigma](n)+k) then return k; end if; end do: end proc: seq(A382483(n),n=1..50) ; # R. J. Mathar, Apr 01 2025
isp(x) = if (x>0, sigma(x) == 2*x); a(n) = my(k=0, s=sigma(n)); while (!(isp(s-k) || isp(s+k)), k++); k; \\ Michel Marcus, Apr 01 2025
a(10) = 0, because 10 + sigma(10) = 28, which is perfect. a(12) = 456, because 456 + 12 + sigma(12) = 496, which is perfect. As 496 is the smallest perfect number at least as large as sigma(60) + 60 = 168 + 60 = 228 we have a(60) = 496 - 228 = 268. - _David A. Corneth_, Apr 10 2025
Do[k=0;s=DivisorSigma[1,n];While[DivisorSigma[1,s+n+k]!=2*(s+n+k),k++];a[n]=k,{n,60}];Array[a,60] (* James C. McMahon, Apr 10 2025 *)
a(n) = my(k=0); while (sigma(k+n+sigma(n)) != 2*(k+n+sigma(n)), k++); k; \\ Michel Marcus, Apr 09 2025
a(n) = {my(s = sigma(n) + n);
forprime(p = 2, oo,
my(c = 2^p-1);
if(isprime(c) && binomial(c+1, 2) >= s,
return(binomial(c+1, 2) - s)))
} \\ David A. Corneth, Apr 10 2025
a(n) = my(v = [6, 28, 496, 8128, 33550336, 8589869056], x=n+sigma(n), k=0); for (i=1, #v-1, if ((x > v[i]) && (x <= v[i+1]), k = i; break)); v[k+1] - x; \\ Michel Marcus, Apr 11 2025
Comments