cp's OEIS Frontend

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.

Showing 1-4 of 4 results.

A064597 Nonunitary abundant numbers: the sum of the nonunitary divisors of n is larger than n; i.e., sigma(n) - usigma(n) > n.

Original entry on oeis.org

36, 48, 72, 80, 96, 108, 120, 144, 160, 168, 180, 192, 200, 216, 224, 240, 252, 264, 280, 288, 300, 312, 320, 324, 336, 352, 360, 384, 392, 396, 400, 408, 416, 432, 448, 456, 468, 480, 504, 528, 540, 552, 560, 576, 588, 600, 612, 624, 640, 648, 672, 684
Offset: 1

Views

Author

Dean Hickerson, Sep 25 2001

Keywords

Examples

			The sum of the nonunitary divisors of 36 is 2 + 3 + 6 + 12 + 18 = 41.

Links

Crossrefs

Cf. A048146, A063846, A064591, A064598.

Programs

  • Mathematica
    nusigma[ n_ ] := DivisorSigma[ 1, n ]-Times@@(1+Power@@#&/@FactorInteger[ n ]); For[ n=1, True, n++, If[ nusigma[ n ]>n, Print[ n ] ] ]
  • PARI
    usigma(n)= { local(f,s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) } { n=0; for (m=1, 10^9, if (sigma(m) - usigma(m) > m, write("b064597.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 19 2009

A063870 Numbers n such that sigma(n) - usigma(n) = 3n/2.

Original entry on oeis.org

480, 2688, 2095104, 16854816, 41055200, 1839272960, 5905219584, 204004720640
Offset: 1

Views

Author

Jason Earls, Aug 27 2001

Keywords

Crossrefs

Cf. A034448, A000203, A048146, A063846, A064591.

Programs

  • PARI
    u(n) = sumdiv(n,d, if(gcd(d,n/d)==1,d)); for(n=1,10000, if(sigma(n)-u(n)==3*n/2,print(n)))

Extensions

More terms from Dean Hickerson, Sep 25 2001
There are no others less than 1.5*10^13, but here's a larger one: 948990933336933380096. - Dean Hickerson, Sep 25 2001

A063875 Numbers k such that sigma(k) - usigma(k) > 3k.

Original entry on oeis.org

831600, 1058400, 1587600, 1663200, 1814400, 1940400, 1965600, 2116800, 2328480, 2494800, 2570400, 2646000, 2721600, 2872800, 2910600, 2948400, 3024000, 3175200, 3326400, 3528000, 3603600, 3628800, 3704400, 3880800, 3931200
Offset: 1

Views

Author

Jason Earls, Aug 27 2001

Keywords

Links

Crossrefs

Cf. A034448, A048146, A034683, A063846.

Programs

  • PARI
    u(n) = sumdiv(n,d, if(gcd(d,n/d)==1,d));
for(n=1,10^9, if(sigma(n)-u(n)>3*n,print(n)))
  • PARI
    u(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))
{ n=0; for (m=1, 10^9, if(sigma(m) - u(m) > 3*m, write("b063875.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 01 2009

Extensions

a(20)-a(25) from Harry J. Smith, Sep 01 2009

A348521 Numbers k such that A348271(k) > 2*k.

Original entry on oeis.org

3600, 5040, 6480, 7056, 7920, 9072, 9360, 11088, 11520, 12240, 13680, 14400, 16128, 16560, 18000, 20880, 22320, 25200, 32400, 35280, 39600, 44100, 45360, 46800, 55440, 56700, 57600, 58320, 58800, 61200, 63504, 65520, 68400, 69300, 71280, 75600, 77616, 79380, 80640
Offset: 1

Views

Author

Amiram Eldar, Oct 21 2021

Keywords

Comments

Odd terms exist (e.g., 349476304574870948475). What is the smallest odd term?

Examples

			3600 is a term since the sum of the noninfinitary divisors of 3600 is A348271(3600) = 8073 > 2*3600 = 7200.

Links

Crossrefs

Cf. A348271, A348274.
Similar sequence: A063846.

Programs

  • Mathematica
    f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := DivisorSigma[1,n] - isigma[n]; Select[Range[10^5], s[#] > 2*# &]
Showing 1-4 of 4 results.

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