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

1,2

Links

Table of n, a(n) for n=1..35.

Formula

a(n) = n * A256527(n). - Max Alekseyev, Sep 29 2023

Example

For n=11, the least number is 1848. In fact, sigma(1848/11) = phi(1848) = 480.

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);

Prog

(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
(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

Crossrefs

Cf. A000010, A000203, A087979.

Sequence in context: A321058 A342827 A264438 * A343424 A041241 A304015

Adjacent sequences: A241759 A241760 A241761 * A241763 A241764 A241765

Keyword

nonn

Author

Paolo P. Lava, Apr 28 2014

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

Status

approved