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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A064549 a(n) = n * Product_{primes p|n} p. 20
1, 4, 9, 8, 25, 36, 49, 16, 27, 100, 121, 72, 169, 196, 225, 32, 289, 108, 361, 200, 441, 484, 529, 144, 125, 676, 81, 392, 841, 900, 961, 64, 1089, 1156, 1225, 216, 1369, 1444, 1521, 400, 1681, 1764, 1849, 968, 675, 2116, 2209, 288, 343, 500, 2601, 1352 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Index of first occurrence of n in A003557. - Franklin T. Adams-Watters, Jul 25 2014

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

FORMULA

Multiplicative with a(p^k)=p^(k+1) when k>0.

a(n) = n*A007947(n) = n^2/A003557(n).

Dirichlet convolution of A000027 and A202535. - R. J. Mathar, Dec 20 2011

a(n) = A078310(n) - 1. - Reinhard Zumkeller, Jul 23 2013

A003557(a(n)) = n; a(A003557(n)) = A057521(n). - Antti Karttunen, Aug 30 2018

G.f.: Sum_{k>=1} mu(k)^2*phi(k)*k*x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Nov 02 2018

EXAMPLE

a(12)=72 since 12=2^2*3 and 12*2*3 = 72.

MAPLE

a:= n -> n * convert(numtheory:-factorset(n), `*`):

seq(a(n), n=1..100); # Robert Israel, Jul 25 2014

MATHEMATICA

a[n_] := n * Times @@ FactorInteger[n][[All, 1]]; Array[a, 100] (* Jean-Fran├žois Alcover, Feb 17 2017 *)

PROG

(PARI) popf(n)= { local(f, p=1); f=factor(n); for(i=1, matsize(f)[1], p*=f[i, 1]); return(p) } { for (n=1, 1000, write("b064549.txt", n, " ", n*popf(n)) ) } \\ Harry J. Smith, Sep 18 2009

(PARI) A064549(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2]++); factorback(f); }; \\ Antti Karttunen, Aug 30 2018

(Haskell)

a064549 n = a007947 n * n  -- Reinhard Zumkeller, Jul 23 2013

(MAGMA) [n^2/( (&+[Floor(k^n/n)-Floor((k^n - 1)/n) : k in [1..n]]) ): n in [1..50]]; // G. C. Greubel, Nov 02 2018

CROSSREFS

A permutation of the powerful numbers A001694.

Cf. A003557 (a left inverse), A007947, A057521, A078310, A202535.

Sequence in context: A050399 A072995 A073395 * A304203 A087687 A264090

Adjacent sequences:  A064546 A064547 A064548 * A064550 A064551 A064552

KEYWORD

mult,nonn,changed

AUTHOR

Henry Bottomley, Oct 16 2001

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 13:54 EST 2018. Contains 317239 sequences. (Running on oeis4.)