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 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

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Last modified July 15 20:24 EDT 2019. Contains 325056 sequences. (Running on oeis4.)