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.

A104904 Numbers n such that d(n)*pi(n)=n, where d(n) is the number of positive divisors of n.

Original entry on oeis.org

2, 8408, 481044, 189961452, 75370122528, 75370124832, 4086199302976, 221945984411264
Offset: 1

Views

Author

Farideh Firoozbakht, Apr 12 2005

Keywords

Comments

Next term is greater than 3*10^9.

Examples

			189961452 is in the sequence because d(189961452)=18; pi(189961452)=10553414 & 18*10553414=189961452.

Crossrefs

Cf. A063903, A104905, A104906.

Programs

  • Mathematica
    Do[If[DivisorSigma[0, n]*PrimePi[n] == n, Print[n]], {n, 2000000000}]

Extensions

a(5)-a(8) from Donovan Johnson, Dec 08 2009

A104906 Numbers n such that d(n)*reversal(n)=phi(n), where d(n) is number of positive divisors of n.

Original entry on oeis.org

1, 10, 831, 8310
Offset: 1

Views

Author

Farideh Firoozbakht, Apr 14 2005

Keywords

Comments

If n is a term of this sequence and gcd(10,n)=1 then 10*n is also in the sequence because reversal(10*n)=reversal(n); d(10)=phi(10) and both functions d & phi are multiplicative. No further terms up to 350000000.
a(5) > 10^12. - Giovanni Resta, Apr 25 2017

Examples

			8310 is in the sequence because d(8310)=16; reversal(8310)=138;
phi(8310)=2208 & 16*138=2108.

Crossrefs

Cf. A063903, A104904, A104905, A104907.

Programs

  • Mathematica
    reversal[n_]:= FromDigits[Reverse[IntegerDigits[n]]]; Do[If[DivisorSigma[0, n]*reversal[n] == EulerPhi[n], Print[n]], {n, 350000000}]

A107656 Numbers k such that prime(k) = d(k)*phi(k) + 1, where d(k) is number of positive divisors of k.

Original entry on oeis.org

1, 2, 3, 4, 652245
Offset: 1

Views

Author

Farideh Firoozbakht, Jun 06 2005

Keywords

Comments

There is no further term up to 5*10^7.
a(6) > 10^10, if it exists. - Amiram Eldar, Apr 30 2024

Examples

			652245 is in the sequence because prime(652245) = d(652245)*phi(652245) + 1.

Crossrefs

Cf. A000005, A000010, A104905, A107657.

Programs

  • Mathematica
    Do[If[Prime[n] == DivisorSigma[0, n]*EulerPhi[n] + 1, Print[n]], {n, 50000000}]
  • PARI
    lista(pmax) = {my(k = 0, f); forprime(p=1, 1e16, k++; f = factor(k); if(p == numdiv(f)*eulerphi(f)+1, print1(k,", ")));} \\ Amiram Eldar, Apr 30 2024
Showing 1-3 of 3 results.

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

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