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 1-3 of 3 results.

A048748 Mean integral divisors associated with A048747.

Original entry on oeis.org

3, 6, 7, 8, 9, 10, 12, 15, 14, 13, 18, 19, 20, 24, 21, 27, 33, 30, 28, 32, 36, 26, 38, 35, 45, 42, 39, 44, 40, 51, 48, 54, 31, 60, 49, 63, 61, 62, 57, 56, 68, 78, 52, 72, 81, 66, 64, 74, 70, 80, 84, 96, 76, 65, 99, 90, 105, 98, 88, 114, 102, 93, 104, 108, 123, 110, 126, 100
Offset: 1

Views

Author

Enoch Haga

Keywords

Examples

			For a(3)=7, n=20 and sum of divisors of 20 is 42, number of divisors is 6, so integral quotient is 7 (42/6).

Links

Crossrefs

Cf. A000005, A000203, A048747.

Formula

a(n) = A000203(A048747(n))/A000005(A048747(n)). - Amiram Eldar, Sep 06 2019

Extensions

Offset corrected by Amiram Eldar, Sep 06 2019

A048751 Composites k whose product of divisors divided by number of divisors is an integer.

Original entry on oeis.org

6, 8, 9, 10, 12, 14, 18, 22, 24, 26, 30, 34, 36, 38, 40, 42, 46, 54, 56, 58, 60, 62, 66, 70, 72, 74, 78, 80, 82, 84, 86, 88, 90, 94, 96, 102, 104, 106, 108, 110, 114, 118, 120, 122, 126, 128, 130, 132, 134, 136, 138, 142, 146, 150, 152, 154, 156, 158, 166, 168, 170
Offset: 1

Views

Author

Enoch Haga, Dec 11 1999

Keywords

Comments

Sequence is identical to A120736 except that it does not include terms 1 and 2, which are not composite. Michel Marcus, Jun 06 2014

Examples

			For k=8, product of divisors is 8*4*2*1=64; number of divisors = 4; 64/4 = 16 (an integer), so 8 is a term.

Links

Crossrefs

Cf. A048747, A048752.

Programs

  • Mathematica
    Select[Range[200],CompositeQ[#]&&IntegerQ[(Times@@Divisors[#])/ DivisorSigma[ 0,#]]&] (* Harvey P. Dale, Aug 21 2021 *)
  • PARI
    isok(n) = (n!=1) && ! isprime(n) && (d = divisors(n)) && ((prod(i=1, #d, d[i]) % numdiv(n)) == 0); \\ Michel Marcus, Jun 05 2014
  • PARI
    is(n)=my(f=factor(n)); n>5 && !isprime(n) && if(gcd(f[,2])%2, n^(numdiv(f)/2), sqrtint(n)^numdiv(f))%numdiv(f)==0 \\ Charles R Greathouse IV, Jun 06 2014

Extensions

Corrected by Michel Marcus, Jun 05 2014

A048749 Factor n, divide sum of aliquot divisors by number of aliquot divisors; append n to sequence if quotient is integral and not previously seen.

Original entry on oeis.org

6, 15, 30, 33, 44, 49, 51, 69, 81, 87, 114, 117, 120, 123, 124, 141, 159, 164, 170, 177, 213, 244, 249, 252, 267, 270, 276, 282, 284, 303, 320, 321, 339, 345, 366, 393, 404, 411, 427, 447, 462, 501, 511, 513, 519, 524, 529, 534, 537, 570, 573, 590, 591, 604
Offset: 1

Views

Author

Enoch Haga

Keywords

Examples

			a(2)=15; for n=15 the sum of aliquot divisors is 9; number of aliquot divisors is 3; 9/3=3. The quotient 3 is the mean aliquot divisor and this is the first time that 3 has occurred.

Links

Crossrefs

Cf. A001065, A023883, A032741, A048747.

Programs

  • Mathematica
    (Select[{Mean[Most[Divisors[#]]], #}& /@ Select[Range[300], CompositeQ], IntegerQ[#[[1]]]&] // Sort // Split[#, #1[[1]] == #2[[1]]&]&)[[All, 1]][[All, 2]] // Sort (* Amiram Eldar, Sep 06 2019 after Jean-François Alcover at A048747 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.