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.

A110084 Numbers n with even length such that sigma(n)=d_1^d_2*d_3^d_4 *...*d_(k-1)^d_k where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

146710, 334552, 12931485, 15734393, 16839254, 20499191, 28661422, 38722820, 43681330, 44463034, 45509442, 55188392, 55938216, 92505149, 1054662422, 1060804965, 1068721252, 1094834272, 1167528360, 1341465139, 1436725284, 1452198772, 1452847236, 1540709585, 1594291529, 1596602643, 1672853710
Offset: 1

Views

Author

Farideh Firoozbakht, Aug 26 2005

Keywords

Examples

			45509442 is in the sequence because sigma(55938216)=5^5*9^3*8^2*1^6.

Links

Crossrefs

Cf. A112009, A112010, A112011.

Programs

  • Mathematica
    Do[h = IntegerDigits[n]; k = Length[h]; If[EvenQ[k] && Select[ Range[k/2], h[[2#-1]] == 0 &] == {} && DivisorSigma[1, n]== Product[h[[2j-1]]^h[[2j]], {j, k/2}], Print[n]], {n, 10^8}]

Extensions

Terms a(14) onward from Max Alekseyev, Oct 16 2012

A112009 Numbers n with even length such that phi(n)=d_1^d_2*d_3^d_4*...* d_(k-1)^d_k where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

113724, 116680, 126620, 176453, 236520, 12146841, 12514635, 13334445, 13469331, 13813728, 16473510, 18259344, 20116537, 20119347, 21324832, 23336066, 27923616, 30352728, 34425425, 35424571, 36311184, 37837170, 39171345, 43362816, 45429360, 45449216, 45916416, 46544032, 50713684, 50816880, 61642672, 62193744, 62226711, 62263890, 62288272, 64245272, 64808352, 64832560, 66707233, 66807126, 66827180, 81913446, 84943040
Offset: 1

Views

Author

Farideh Firoozbakht, Aug 26 2005

Keywords

Examples

			27923616 is in the sequence because phi(27923616)=2^7*9^2*3^6*1^6.
11600069 and 23635500 are not members, since 0^0 is undefined.

Crossrefs

Cf. A110084, A112010, A112011.

Programs

  • Mathematica
    Do[h = IntegerDigits[n]; k = Length[h]; If[EvenQ[k] && Select[ Range[k/2], h[[2#-1]] == 0 &] == {} && EulerPhi[n]==Product[ h[[2j-1]]^h[[2j]], {j, k/2}], Print[n]], {n, 30000000}]

Extensions

Edited by N. J. A. Sloane, Apr 02 2009
More terms from Max Alekseyev, Oct 16 2012

A112010 Numbers m with even length such that phi(m)=phi(d_1^d_2*d_3^d_4*...* d_(k-1)^d_k) where d_1 d_2 ... d_k is the decimal expansion of m.

Original entry on oeis.org

24, 1064, 2592, 6520, 106434, 145166, 237165, 262535, 372780, 491520, 531765, 546410, 566250, 636352, 12716544, 12806910, 13666320, 15116832, 15408692, 17473715, 21645616, 23473515, 23726640, 23728264, 26722436, 26757024, 27933192, 30537364, 30869280, 32118177, 33452293, 34114338, 39602752, 42262365, 44373490
Offset: 1

Views

Author

Farideh Firoozbakht, Aug 26 2005

Keywords

Examples

			33452293 is in the sequence because phi(33452293)=phi(3^3*4^5*2^2*9^3).

Crossrefs

Cf. A110084, A112009, A112011.

Programs

  • Mathematica
    Do[h = IntegerDigits[n]; k = Length[h]; If[EvenQ[k] && Select[ Range[k/2], h[[2#-1]] == 0 &] == {} && EulerPhi[n]==EulerPhi [Product[h[[2j-1]]^h[[2j]], {j, k/2}]], Print[n]], {n, 31000000}]
epQ[n_]:=Module[{idn=IntegerDigits[n]},EvenQ[Length[idn]]&& FreeQ[ Take[ idn, {1,-1,2}],0] && EulerPhi[n] == EulerPhi[Times@@(#[[1]]^#[[2]]&/@ Partition[ idn,2])]]; Join[Select[Range[10,99],epQ],Select[Range[ 1000,9999], epQ], Select[Range[100000,999999],epQ], Select[Range[ 10000000, 44999999], epQ]] (* Harvey P. Dale, Feb 24 2016 *)

Extensions

More terms from Max Alekseyev, Oct 16 2012
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.