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.

A228299 Composite squarefree numbers n such that p+d(n) divides n+d(n), where p are the prime factors of n and d(n) the number of divisors of n.

Original entry on oeis.org

21098, 134930, 343027, 361730, 387127, 751394, 793595, 1344517, 1430449, 1579394, 1794854, 3542797, 5022254, 7930117, 9241627, 12122947, 21089129, 21928717, 49825117, 70233329, 78795074, 90079589, 95208734, 110995807, 124648303, 124964219, 144871634
Offset: 1

Views

Author

Paolo P. Lava, Aug 20 2013

Keywords

Comments

Subsequence of A120944.

Examples

			Prime factors of 21098 are 2, 7, 11 and 137 while d(21098) = 16. We have that 21098 + 16 = 21114 and 21114 / (2 + 16) =  1173, 21114 / (7 + 16) = 918, 21114 / (11 + 16) = 782 and 21114 / (137 + 16) = 138.

Links

Crossrefs

Cf. A000005, A228300-A228302.

Programs

  • Maple
    with (numtheory); P:=proc(q) local a,i,ok,n;
for n from 1 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
for i from 1 to nops(a) do if a[i][2]>1 then ok:=0; break;
else if not type((n+tau(n))/(a[i][1]+tau(n)),integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^6);

Extensions

More terms from Michel Marcus, Sep 21 2013
Deleted first term from Paolo P. Lava, Sep 23 2013

A229273 Composite squarefree numbers n such that p-tau(n) divides n-sigma(n), where p are the prime factors of n, tau(n) = A000005(n) and sigma(n) = A000203(n).

Original entry on oeis.org

6, 10, 15, 22, 78, 138, 273, 483, 3243, 3913, 104377, 477337, 1537627, 1904487, 2508961, 3326829, 3716167, 5148949, 6154017, 6686113, 11521842, 14355679, 16872583, 25165777, 28029883, 31232337, 32403342, 50725419, 57396469, 68815381, 86850249, 98242959
Offset: 1

Views

Author

Paolo P. Lava, Sep 19 2013

Keywords

Comments

Subsequence of A120944.

Examples

			Prime factors of 273 are 3, 7, 13 and sigma(273) = 448, tau(273) = 8.
273 - 448 = -175 and (-175) / (3 - 8) = 35, (-175) / (7 - 8) = 175, (-175) / (13 - 8) = -35.

Crossrefs

Cf. A000005, A000203.
Cf. A228299, A228300, A228301, A228302, A229274, A229275, A229276.

Programs

  • Maple
    with (numtheory); P:=proc(q) local a, b, c, i, ok, p, n;
for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;
else if not type((n-sigma(n))/(a[i][1]-tau(n)), integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(2*10^6);

Extensions

a(20)-a(33) from Giovanni Resta, Sep 20 2013
First term deleted by Paolo P. Lava, Sep 23 2013

A229274 Composite squarefree numbers n such that p+tau(n) divides n-sigma(n), where p are the prime factors of n, tau(n) = A000005(n) and sigma(n) = A000203(n).

Original entry on oeis.org

51, 93, 177, 219, 303, 471, 597, 681, 723, 807, 849, 933, 1059, 1101, 1227, 1437, 1563, 1689, 1731, 1857, 1941, 1983, 2319, 2361, 2487, 2571, 2823, 2949, 2991, 3117, 3327, 3369, 3453, 3579, 3747, 3831, 3873, 3957, 4083, 4377, 4461, 4629, 4713, 4839, 4881
Offset: 1

Views

Author

Paolo P. Lava, Sep 19 2013

Keywords

Comments

Subsequence of A120944.

Examples

			Prime factors of 177 are 3, 59 and sigma(177) = 240 , tau(177) = 4.
177 - 240 = -63 and (-63) / (3 + 4) = -9, (-63) / (59 + 4) = -1.

Links

Crossrefs

Cf. A000005, A000203.
Cf. A228299, A228300, A228301, A228302, A229273, A229275, A229276.

Programs

  • Maple
    with (numtheory); P:=proc(q) local a, b, c, i, ok, p, n;
for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
for i from 1 to nops(a) do if a[i][2]>1 then ok:=0; break;
else if not type((n-sigma(n))/(a[i][1]+tau(n)), integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^6);

Extensions

First term deleted by Paolo P. Lava, Sep 23 2013

A228301 Composite squarefree numbers n such that p-d(n) divides n+d(n), where p are the prime factors of n and d(n) the number of divisors of n.

Original entry on oeis.org

6, 10, 14, 15, 35, 70, 154, 190, 322, 385, 442, 595, 682, 2737, 3619, 14986, 15314, 19019, 24817, 26767, 33626, 78387, 85034, 130169, 155363, 166934, 189727, 214107, 225029, 238901, 243217, 285934, 381547, 395219, 415679, 417989, 455609, 466193, 544918
Offset: 1

Views

Author

Paolo P. Lava, Aug 20 2013

Keywords

Comments

Subsequence of A120944.

Examples

			Prime factors of 19019 are 7, 11, 13 and 19 while d(19019) = 16. We have that 19019 + 16 = 19035 and 19035 / (7 - 16) =  -2115, 19035 / (11 - 16) =  -3807, 19035 / (13 - 16) = -6345 and 19035 / (19 - 16) = 6345.

Links

Crossrefs

Cf. A000005, A228299, A228300, A228302.

Programs

  • Maple
    with (numtheory); P:=proc(q) local a,b,c,i,ok,p,n;
for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;
else if not type((n+tau(n))/(a[i][1]-tau(n)),integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^6);

Extensions

First term deleted by Paolo P. Lava, Sep 23 2013
Showing 1-4 of 4 results.

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