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.

A251361 Numbers k such that pi(k) is the concatenation of distinct prime factors of k, in increasing order.

Original entry on oeis.org

4, 100, 31509, 7560625
Offset: 1

Views

Author

Jahangeer Kholdi, Dec 02 2014

Keywords

Comments

Next term must be greater than 4*10^8.
Numbers k such that A000720(k) = A084317(k). - Michel Marcus, Dec 06 2014

Examples

			4 is in the sequence since 4=2^2 and pi(4)=2,
100 is in the sequence since 100=2^2*5^2 and pi(100)=25,
31509 is in the sequence since 31509=3^4*389 and pi(31509)=3389, and
7560625 is in the sequence since 7560625=5^4*12097 and pi(7560625)=512097.
		

Crossrefs

Programs

  • Mathematica
    a251361[n_Integer] := Select[Range[n], PrimePi[#] == FromDigits[
    Flatten@ IntegerDigits[First@ Transpose@ FactorInteger[#]]] &]; a251361[10^6] (* Michael De Vlieger, Dec 03 2014 *)
  • PARI
    is(n)=eval(fold((x,y)->Str(x,y),factor(n)[,1]))==primepi(n) \\ Charles R Greathouse IV, Dec 06 2014

Extensions

Definition corrected by Max Alekseyev, Feb 12 2025

A251362 Numbers n such that n is the concatenation of distinct prime factors of phi(n), in increasing order.

Original entry on oeis.org

25, 235741, 23517131, 274873357929, 2357131984859
Offset: 1

Views

Author

Jahangeer Kholdi, Dec 03 2014

Keywords

Comments

Numbers n such that n = A084317(A000010(n)). - Michel Marcus, Dec 06 2014

Examples

			25 is in the sequence since phi(25)=2^2*5,
235741 is in the sequence since phi(235741)=2^4*3^2*5*7*41,
23517131 is in the sequence since phi(23517131)=2^7*3*5^2*17*131.
		

Crossrefs

Programs

  • Mathematica
    a251362[n_Integer] := Rest@ Select[Range[n], # ==
    FromDigits[Flatten@IntegerDigits[First@Transpose@FactorInteger[EulerPhi[#]]]] &]; a251362[10^6] (* Michael De Vlieger, Dec 03 2014 *)

Extensions

a(4)-a(5) from Max Alekseyev, Feb 11 2025

A251363 Numbers n such that n is the concatenation of distinct prime factors of phi(n), in decreasing order.

Original entry on oeis.org

237532, 832332, 82953292, 423238803752
Offset: 1

Views

Author

Jahangeer Kholdi, Dec 03 2014

Keywords

Comments

Numbers n such that n = A085307(A000010(n)). - Michel Marcus, Dec 06 2014

Examples

			237532 is in the sequence since phi(237532)=23*7*5*3^2*2^4,
832332 is in the sequence since phi(832332)=83*23*3^2*2^4, and
82953292 is in the sequence since phi(82953292)=829*53*29*2^5.
		

Crossrefs

Programs

  • Mathematica
    a251363[n_Integer] :=
    Rest@ Select[Range[n], # == FromDigits[Flatten@ IntegerDigits[
    Sort[First@ Transpose@ FactorInteger[EulerPhi[#]], Greater]]] &]; a251363[10^6] (* Michael De Vlieger, Dec 03 2014 *)

Extensions

a(4) from Max Alekseyev, Feb 10 2025
Showing 1-3 of 3 results.