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.

A228302 Composite squarefree numbers n such that p+d(n) divides n-d(n) for all prime factors p of n, where d(n) is the number of divisors of n.

Original entry on oeis.org

4958, 51653, 55583, 1251574, 4909102, 5430797, 5785073, 6096931, 13892243, 14058781, 14809517, 16699426, 27391073, 32426566, 32673383, 38669686, 43459682, 44762461, 53638783, 69836866, 74975761, 75226313, 85607461, 96973703, 105139141, 122864065
Offset: 1

Views

Author

Paolo P. Lava, Aug 20 2013

Keywords

Comments

Subsequence of A120944.

Examples

			Prime factors of 51653 are 7, 47 and 157 while d(51653) = 8. We have that 51653 - 8 = 51645 and 51645 / (7 + 8) =  3443, 51645 / (47 + 8) = 939 and 51645 / (157 + 8) = 313.

Links

Crossrefs

Cf. A000005, A228299-A228301.

Programs

  • Maple
    with(numtheory);  P:=proc(q) local a,i,ok,p,n;
for n from 1 to q do if not isprime(n) and issqrfree(n) then
a:=ifactors(n)[2]; ok:=1; for i from 1 to nops(a) do
if not type((n-tau(n))/(a[i][1]+tau(n)),integer) then ok:=0; break; fi; od;
if ok=1 then print(n); fi; fi; od; end: P(10^9);

Extensions

More terms from Michel Marcus, Sep 21 2013
First term deleted by 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

A228300 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, 15, 110, 170, 273, 638, 935, 1394, 2093, 2438, 2465, 4823, 5453, 7973, 11978, 16354, 17963, 34918, 43337, 46943, 62491, 64583, 68266, 71603, 72046, 74347, 75361, 85877, 134458, 148291, 155933, 186235, 188071, 201994, 209933, 280891, 307021, 367081
Offset: 1

Views

Author

Paolo P. Lava, Aug 20 2013

Keywords

Comments

Subsequence of A120944.

Examples

			Prime factors of 17963 are 11, 23 and 71 while d(17963) = 8. We have that 17963 - 8 = 17955 and 17955 / (11 - 8) =  5985, 17955 / (23 - 8) = 1197 and 17955 / (71 - 8) = 285.

Links

Crossrefs

Cf. A000005, A228299, A228301, 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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