The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A020491 Numbers k such that sigma_0(k) divides phi(k). 14
 1, 3, 5, 7, 8, 9, 10, 11, 13, 15, 17, 18, 19, 21, 23, 24, 26, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 43, 45, 47, 49, 51, 52, 53, 55, 56, 57, 58, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 82, 83, 84, 85, 87, 88, 89, 90, 91, 93, 95, 97, 98, 99, 101, 102, 103, 104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In other words, numbers k such that d(k) divides phi(k). From Enrique Pérez Herrero, Aug 11 2010: (Start) sigma_0(k) divides phi(k) when: k is an odd prime: A065091; k is an odd squarefree number: A056911; k = 2^m, where m <> 1 is a Mersenne number (A000225). If d divides (p-1), with p prime, then p^(d-1) is in this sequence, as are p^(p-1), p^(p-2) and p^(-1+p^n). (End) phi(n) and d(n) are multiplicative functions, so if m and n are coprime and both of them are in this sequence then m*n is also in this sequence. - Enrique Pérez Herrero, Sep 05 2010 From Bernard Schott, Aug 14 2020: (Start) The corresponding quotients are in A289585. About the 3rd case of Enrique Pérez Herrero's comment: if k = 2^M_m, where M_m = 2^m - 1 is a Mersenne number >= 3 (A000225), then the corresponding quotient phi(k)/d(k) is the integer 2^(2^m-m-2) = A076688(m); hence, these numbers k, A058891 \ {2}, form a subsequence. (End) LINKS Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000 Psychedelic Geometry Blogspot, Fermat and Mersenne Numbers Conjecture-(2) MAPLE with(numtheory); A020491:=proc(q) local n; for n from 1 to q do if (phi(n) mod tau(n))=0 then print(n); fi; od; end: A020491(1000000); # Paolo P. Lava, Jan 31 2013 MATHEMATICA Select[ Range[ 105 ], IntegerQ[ EulerPhi[ # ]/DivisorSigma[ 0, # ] ]& ] PROG (PARI) isok(k) = !(eulerphi(k) % numdiv(k)); \\ Michel Marcus, Aug 10 2020 CROSSREFS Cf. A000005, A000010. Complement of A015733. [Enrique Pérez Herrero, Aug 11 2010] Cf. A058891, A076688, A289585. Sequence in context: A141114 A136443 A247459 * A168501 A173186 A335575 Adjacent sequences:  A020488 A020489 A020490 * A020492 A020493 A020494 KEYWORD nonn AUTHOR 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.

Last modified June 19 13:02 EDT 2021. Contains 345129 sequences. (Running on oeis4.)