login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244069 Consider a number of k digits n = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1). Sequence lists the numbers n such that Sum_{i=1..k-1}{phi(Sum_{j=1..i}{d_(j)*10^(j-1)})}} = Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below). 3
11, 21, 53, 75, 83, 95, 211, 506, 523, 708, 908, 932, 955, 1008, 5086, 6535, 7272, 7557, 9126, 20534, 31165, 51301, 52695, 71665, 73713, 85173, 90902, 93026, 93565, 210021, 313370, 330173, 406945, 423775, 521427, 633190, 728687, 850123, 926281 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No single-digit terms are permitted. - Harvey P. Dale, Mar 08 2015

LINKS

Table of n, a(n) for n=1..39.

EXAMPLE

If n = 423775, starting from the least significant digit, let us cut the number into the set {5, 75, 775, 3775, 23775}. We have:

sigma(5) = 6;

sigma(75) = 124;

sigma(775) = 992;

sigma(3775) = 4712;

sigma(23775) = 39432.

Then, starting from the most significant digit, let us cut the number into the set {4, 42, 423, 4237, 42377}. We have:

phi(4) = 2;

phi(42) = 12;

phi(423) = 276;

phi(4237) = 3996;

phi(42377) = 40980.

Finally, 6 + 124 + 992 + 4712 + 39432 = 2 + 12 + 276 + 3996 + 40980 = 45266.

MAPLE

with(numtheory); P:=proc(q) local a, b, k, n; for n from 10 to q do

a:=0; k:=1; while trunc(n/10^k)>0 do a:=a+phi(trunc(n/10^k)); k:=k+1; od;

b:=0; k:=1; while (n mod 10^k)<n do b:=b+sigma(n mod 10^k); k:=k+1; od;

if a=b then print(n); fi; od; end: P(10^9);

MATHEMATICA

dsepQ[n_]:=Module[{idn=IntegerDigits[n], len}, len=Length[idn]-1; Total[ DivisorSigma[1, #]&/@(FromDigits/@Table[Take[idn, -k], {k, If[Last[idn] == 0, 2, 1], len}])]==Total[EulerPhi/@(FromDigits/@Table[Take[idn, i], {i, len}])]]; Select[Range[10, 10^6], dsepQ] (* Harvey P. Dale, Mar 08 2015 *)

CROSSREFS

Cf. A000010, A000203, A240894-A240903, A241207, A241502, A241503, A244068.

Sequence in context: A127624 A097616 A146150 * A058489 A278780 A071158

Adjacent sequences:  A244066 A244067 A244068 * A244070 A244071 A244072

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Jun 19 2014

EXTENSIONS

Corrected (a(18) added) by Harvey P. Dale, Mar 08 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)