A078310 a(n) = n*rad(n) + 1, where rad = A007947 (squarefree kernel).

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

Offset

1,1

Comments

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

Formula

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

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 * A359487 A138848 A194350

Adjacent sequences: A078307 A078308 A078309 * A078311 A078312 A078313

Keyword

nonn

Author

Reinhard Zumkeller, Nov 23 2002

Status

approved