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A078315
Minimum exponent in prime factorization of n*rad(n)+1, where rad = A007947 (the radical or squarefree kernel).
6
1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,4
COMMENTS
2 = a(4) = a(45) = a(48) = a(140) = a(529) = a(682) = a(3264) = a(3564) = a(4680) = a(4756) = a(166320) = a(194873) = a(330096) = a(364905) = a(2100332) = a(4160200) with all terms in between equal to 1. Is there an n with a(n) > 2? - Charles R Greathouse IV, May 20 2013
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A051904(A078310(n)).
MATHEMATICA
a[n_] := Min[FactorInteger[1 + n * Times @@ FactorInteger[n][[;; , 1]]][[;; , 2]]]; Array[a, 100] (* Amiram Eldar, Sep 08 2024 *)
PROG
(PARI) a(n)=my(f=factor(n)); f[, 2]=apply(n->n+1, f[, 2]); vecmin(factor(factorback(f)+1)[, 2]) \\ Charles R Greathouse IV, May 20 2013
(Haskell)
a078315 = a051904 . a078310 -- Reinhard Zumkeller, Jul 23 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 23 2002
STATUS
approved