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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A078310 a(n) = n*rad(n) + 1, where rad = A007947 (squarefree kernel). 21
2, 5, 10, 9, 26, 37, 50, 17, 28, 101, 122, 73, 170, 197, 226, 33, 290, 109, 362, 201, 442, 485, 530, 145, 126, 677, 82, 393, 842, 901, 962, 65, 1090, 1157, 1226, 217, 1370, 1445, 1522, 401, 1682, 1765, 1850, 969, 676, 2117, 2210, 289, 344, 501, 2602, 1353 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = A064549(n)+1.

A112526(a(n) - 1) = 1, see also A224866. - Reinhard Zumkeller, Jul 23 2013

Increase each exponent in the prime factorization by one, then add 1 to the new product. - M. F. Hasler, Jan 22 2017

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

MAPLE

a:= n-> 1+n*mul(i[1], i=ifactors(n)[2]):

seq(a(n), n=1..60);  # Alois P. Heinz, Jan 22 2017

MATHEMATICA

A078310[n_] := n*Times @@ FactorInteger[n][[All, 1]] + 1; Array[A078310, 50] (* G. C. Greubel, Apr 25 2017 *)

PROG

(Haskell)

a078310 n = n * a007947 n + 1

-- Reinhard Zumkeller, Jul 23 2013, Oct 19 2011

(PARI) rad(n)=my(f=factor(n)[, 1]); prod(i=1, #f, f[i])

a(n)=n*rad(n)+1 \\ Charles R Greathouse IV, Jul 09 2013

(PARI) a(n)={n=factor(n); n[, 2]+=vectorv(matsize(n)[1], i, 1); factorback(n)+1} \\ M. F. Hasler, Jan 22 2017

(PARI) a(n)=prod(k=1, matsize(n=factor(n))[1], n[k, 1]^(n[k, 2]+1))+1 \\ M. F. Hasler, Jan 22 2017

CROSSREFS

Smallest, greatest factor: A078311, A078312, number of factors: A078313, A078314, min, max exponent: A078315, A078316, number, sum of divisors: A078317, A078318, sum of prime factors: A078319, A078320, Euler's totient: A078321, squarefree kernel: A078322, arithmetic derivative: A078323.

Cf. primes: A078324, squarefree: A078325, squareful: A078326.

Sequence in context: A001440 A258779 A097378 * A138848 A194350 A123466

Adjacent sequences:  A078307 A078308 A078309 * A078311 A078312 A078313

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 23 2002

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 August 17 17:02 EDT 2018. Contains 313816 sequences. (Running on oeis4.)