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 1-5 of 5 results.

A137603 Numbers m such that product of factorials of digits of m equals sigma(m).

Original entry on oeis.org

1, 14, 1253, 2261, 2622, 13145, 13630, 20146, 24035, 30362, 31416, 42504, 50424, 63240, 112281, 117124, 126005, 150360, 161160, 225153, 252126, 262105, 318021, 341630, 510632, 611523, 723104, 1071521, 1131190, 1153262, 1200626, 1242108
Offset: 1

Views

Author

Farideh Firoozbakht, Apr 11 2008

Keywords

Examples

			sigma(10230248)=1!*0!*2!*3!*0!*2!*4!*8! so 10230248 is in the sequence.

Links

Crossrefs

Cf. A066457, A066459, A000203.

Programs

  • Mathematica
    Select[Range[1250000],Times@@(IntegerDigits[#]!)==DivisorSigma[1,#]&] (* James C. McMahon, Jun 01 2025 *)

A105327 Numbers n such that pi(n)=pi(d_1!)+pi(d_2!)+...+pi(d_k!) where d_1 d_2 ...d_k is the decimal expansion of n.

Original entry on oeis.org

0, 1, 2, 115, 1626, 5370, 5371, 5570, 5571, 6170, 6171, 40854, 373369, 373469, 419386, 419658, 419685, 889609, 889619
Offset: 1

Views

Author

Farideh Firoozbakht, Apr 20 2005

Keywords

Comments

There is no further term (the proof is easy).

Examples

			889619 is in the sequence because pi(889619)=pi(8!)+pi(8!)+pi(9!)+pi(6!)+pi(1!)+pi(9!).

Links

  • Eric Weisstein's World of Mathematics, Factorial.

Crossrefs

Cf. A066457, A105328.

Programs

  • Mathematica
    Do[h = IntegerDigits[m]; l = Length[h]; If[PrimePi[m] == Sum[PrimePi[h[[k]]! ], {k, l}], Print[m]], {m, 0, 3000000}]

A139182 Numbers m such that pi(m) = d_1!!*d_2!!*...*d_k!! where d_1 d_2 ... d_k is the decimal expansion of m.

Original entry on oeis.org

50, 51, 125, 15405, 26205, 226700, 226701, 226710, 226711, 513090, 513091, 1351832, 8210065
Offset: 1

Views

Author

Farideh Firoozbakht, Apr 19 2008

Keywords

Comments

Numbers m with a product of the double-factorials of the digits equal to A000720(m).
If { m is in the sequence, 10 divides m and m+1 is composite } then m+1 is in the sequence. [Clarified by N. J. A. Sloane, Feb 06 2022]

Examples

			pi(8210065)=8!!*2!!*1!!*0!!*0!!*6!!*5!!.

Crossrefs

Cf. A066457, A006882.

Programs

  • Mathematica
    Select[Range[83*10^5],Times@@(IntegerDigits[#]!!)==PrimePi[#]&] (* Harvey P. Dale, Apr 12 2024 *)

A139408 Numbers n such that phi(n)=d_1!!*d_2!!*...*d_k!! where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

1, 260, 450, 543, 630, 1164, 2080, 3534, 3640, 4525, 5425, 11176, 13365, 15407, 18333, 24056, 24552, 25064, 25452, 26352, 30660, 37324, 45136, 46160, 46325, 49321, 51742, 52080, 54540, 67122, 76041, 76151, 80325, 81060, 81217, 81532
Offset: 1

Views

Author

Farideh Firoozbakht, Apr 19 2008

Keywords

Examples

			phi(1111900875)=1!!*1!!*1!!*1!!*9!!*0!!*0!!*8!!*7!!*5!!, so 1111900875 is in the sequence.

Crossrefs

Cf. A066457, A139182.

A145744 Primes p such that product of factorials of digits of p equals pi(p).

Original entry on oeis.org

13, 226130351
Offset: 1

Views

Author

Farideh Firoozbakht, Oct 22 2008

Keywords

Comments

This sequence is a subsequence of A066457.
a(3) > 10^19 if it exists. - Chai Wah Wu, May 03 2018

Examples

			pi(226130351)=2!*2!*6!*1!*3!*0!*3!*5!*1!.

Links

  • C. Caldwell and G. L. Honaker, Jr., 226130351

Crossrefs

Cf. A066457.
Showing 1-5 of 5 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.