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A120737 Numbers k whose number of divisors d(k) is divisible by every prime factor of k. 6
1, 2, 8, 9, 12, 18, 32, 72, 80, 96, 108, 128, 243, 288, 448, 486, 512, 625, 720, 768, 864, 972, 1152, 1200, 1250, 1620, 1944, 2000, 2025, 2048, 2560, 2592, 3888, 4032, 4050, 4608, 5000, 5625, 6144, 6561, 6912, 7500, 7776, 8192, 8748, 9408, 10800, 11250 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Numbers k such that A000005(k)/A007947(k) is an integer. A070226 is a subsequence of this sequence. Conjecture: If A000005(k) divides A007947(k) for some k, then A007947(k)/A000005(k)=1. - Ctibor O. Zizka, Feb 05 2009
This sequence contains exactly those positive integers k where 1 is the only positive divisor of k that is coprime to d(k). - Leroy Quet, May 23 2009
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..100 from Paolo P. Lava)
EXAMPLE
d(32) = 6. 2 is the only prime dividing 32. 2 divides 6, so 32 is in the sequence.
MAPLE
isA120737 := proc(n) local d, p; d := numtheory[tau](n) ; p := 2 ; while p <= n do if ( n mod p ) = 0 then if ( d mod p ) <> 0 then RETURN(false) ; fi ; fi ; p := nextprime(p) ; od ; RETURN(true) ; end: for n from 1 to 12000 do if isA120737(n) then printf("%d, ", n) ; fi ; od ;
# R. J. Mathar, Aug 17 2006
MATHEMATICA
divQ[n_] := AllTrue[FactorInteger[n][[;; , 1]], Divisible[DivisorSigma[0, n], #] &]; Select[Range[10^4], divQ] (* Amiram Eldar, Nov 08 2020 *)
PROG
(PARI) isok(k) = Mod(numdiv(k), k)^eulerphi(k) == 0; \\ Michel Marcus, May 11 2019
CROSSREFS
Sequence in context: A279373 A057529 A336715 * A081381 A235524 A239133
KEYWORD
nonn
AUTHOR
Leroy Quet, Jun 29 2006
EXTENSIONS
More terms from R. J. Mathar, Aug 17 2006
Name simplified by Jon E. Schoenfield, Mar 03 2019
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)