A241762 a(n) is the least number k > 0 such that sigma(k/n) = phi(k).
1, 2, 45, 12, 70, 36, 42, 336, 270, 420, 1848, 2520, 2730, 5880, 12600, 332640, 353430, 166320, 175560, 1663200, 2522520, 87650640, 118798680, 1051807680, 671517000, 1139458320, 35231316120, 15952416480, 16522145640, 495664369200, 563462139240, 18030788455680, 37620925622280, 130723216303680, 43948907402400
Offset: 1
Keywords
Examples
For n=11, the least number is 1848. In fact, sigma(1848/11) = phi(1848) = 480.
Programs
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Maple
with(numtheory): P:=proc(q) local k,n; for k from 1 to q do for n from k by k to q do if sigma(n/k)=phi(n) then print(n); break; fi; od; od; end: P(10^5);
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PARI
for(k=1,29,n=0;for(i=1,2^64,if(sigma(i)==eulerphi(i*k),n=i*k;break)); print(k," ",n)) \\ Dana Jacobsen, May 02 2014
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Perl
use Math::Prime::Util qw/:all/; for $k (1..29) { $i=1; $i++ while divisor_sum($i) != euler_phi($i*$k); say "$k ",$i*$k; } # Dana Jacobsen, May 02 2014
Formula
a(n) = n * A256527(n). - Max Alekseyev, Sep 29 2023
Extensions
a(22)-a(26) from Giovanni Resta, Apr 29 2014
a(27)-a(29) from Dana Jacobsen, May 02 2014
a(30)-a(35) from Max Alekseyev, Sep 29 2023