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.

A100416 Numbers n such that sum of the proper divisors of n is equal to d_1!+d_2!+...+d_k!, where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

561653, 606061, 1649345, 2631227, 5657101, 25376713, 33805243, 38747603, 68760599, 77773043, 80404183, 101695597, 124781123, 125348239, 142692929, 152212087, 177464929, 184416409, 192144907, 200781041, 238715647, 241253839
Offset: 1

Views

Author

Farideh Firoozbakht, Dec 12 2004

Keywords

Examples

			38747603 is in the sequence because {1,769,50387} is the set of proper
divisors of 38747603 and 3!+8!+7!+4!+7!+6!+0!+3!=1+769+50387.

Crossrefs

Cf. A101697.

Programs

  • Mathematica
    Do[h = IntegerDigits[n]; l = Length[h]; If[DivisorSigma[1, n] - n == Sum[h[[k]]!, {k, l}], Print[n]], {n, 60000000}]
Select[Range[2413*10^5],Total[Most[Divisors[#]]]==Total[ IntegerDigits[ #]!]&] (* Harvey P. Dale, Oct 11 2018 *)

Extensions

a(9)-a(22) from Donovan Johnson, Dec 07 2008
Comment deleted by Harvey P. Dale, Oct 11 2018

A101699 Numbers m such that phi(m) = d_1*d_1!+d_2*d_2!+...+d_k*d_k! where d_1 d_2 ... d_k is the decimal expansion of m.

Original entry on oeis.org

1, 23, 66666, 13179592
Offset: 1

Views

Author

Farideh Firoozbakht, Dec 19 2004

Keywords

Examples

			13179592 is in the sequence because phi(13179592) = 1*1!+3*3!+1*1!+7*7!+9*9!+5*5!+9*9!+2*2!.

Crossrefs

Cf. A101697, A101698.

Programs

  • Mathematica
    Do[If[EulerPhi[n] == Apply[Plus, IntegerDigits[n]*IntegerDigits[n]! ], Print[n]], {n, 30000000}]
Select[Range[132*10^5],EulerPhi[#]==Total[# #!&/@IntegerDigits[#]]&] (* Harvey P. Dale, Mar 06 2023 *)

A101702 Numbers m such that the sum of the factorials of their digits is equal to the reversal of m.

Original entry on oeis.org

1, 2, 541, 52100, 58504, 66410, 430000, 863180, 8601400, 17927300, 27927300, 31000000, 665100000, 3715000000, 6739630000, 11000000000, 21000000000, 53100000000, 70858000000, 79637300000, 451000000000, 1715000000000, 2715000000000, 48304000000000, 340000000000000, 5520000000000000
Offset: 1

Views

Author

Farideh Firoozbakht, Dec 24 2004

Keywords

Comments

If s=sum of the factorials of digits of m & reversal(m) >= s then 10^(reversal(m) - s)*m is in the sequence. Example m=23; s = 2! + 3!; reversal(23) - s = 24 & 23*10^24 is in the sequence. So this sequence is infinite because there exist infinitely many numbers m such that reversal(m) > s. If m is a k-digit term of this sequence and the first digit of m is 1 then 10^(k-1) + m is also in the sequence. Examples: m=1 so 10^(1-1) + 1 = 2 is in the sequence, m=17927300 so 10^7 + 17927300 = 27927300 is in the sequence. If m > 5 then 10 divides a(m). If 10 doesn't divide a(m) then the reversal of m is in the sequence A014080, so all terms of A014080 are: reversal(1), reversal(2), reversal(541) & reversal(58504).

Examples

			665100000 is in the sequence because reversal(665100000) = 1566 = 6! + 6! + 5! + 1! + 0! + 0! + 0! + 0! + 0!.

Crossrefs

Cf. A014080, A049529, A101697.

Programs

  • Mathematica
    Do[h = IntegerDigits[n]; l = Length[h]; If[FromDigits[Reverse[IntegerDigits[n]]] == Sum[h[[k]]!, {k, l}], Print[n]], {n, 10^9}]

Extensions

More terms from Donovan Johnson, Feb 26 2008
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.