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A120454
a(n) = ceiling(GPF(n)/LPF(n)) where GPF is greatest prime factor, LPF is least prime factor.
2
1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 4, 2, 1, 1, 2, 1, 3, 3, 6, 1, 2, 1, 7, 1, 4, 1, 3, 1, 1, 4, 9, 2, 2, 1, 10, 5, 3, 1, 4, 1, 6, 2, 12, 1, 2, 1, 3, 6, 7, 1, 2, 3, 4, 7, 15, 1, 3, 1, 16, 3, 1, 3, 6, 1, 9, 8, 4, 1, 2, 1, 19, 2, 10, 2, 7, 1, 3, 1, 21, 1, 4, 4, 22, 10, 6, 1, 3, 2, 12, 11, 24, 4, 2, 1, 4, 4
OFFSET
1,6
COMMENTS
Given GPF(n) and LPF(n), the sum is A074320, the difference is A046665 and the product is A066048. a(n) = 1 iff n is p^k iff n is in A000961.
LINKS
FORMULA
a(n) = ceiling(A006530(n)/A020639(n)).
a(n) = A069897(n) + 1 if n is not a power of a prime (A024619), and 1 otherwise. - Amiram Eldar, Oct 24 2024
EXAMPLE
a(26) = ceiling(GPF(26)/LPF(26)) = ceiling(13/2) = 7.
MAPLE
A120454 := proc(n) local ifs ; if n = 1 then RETURN(1) ; else ifs := ifactors(n)[2] ; RETURN( ceil(op(1, op(-1, ifs))/op(1, op(1, ifs))) ) ; fi ; end ; for n from 1 to 100 do printf("%d, ", A120454(n)) ; od ; # R. J. Mathar, Dec 16 2006
MATHEMATICA
a[n_] := Module[{p = FactorInteger[n][[;; , 1]]}, Ceiling[p[[-1]] / p[[1]]]]; Array[a, 100] (* Amiram Eldar, Oct 24 2024 *)
PROG
(PARI) A120454(n) = if(1==n, 1, my(f = factor(n), lpf = f[1, 1], gpf = f[#f~, 1]); ceil(gpf/lpf)); \\ Antti Karttunen, Sep 06 2018
KEYWORD
easy,nonn,changed
AUTHOR
Jonathan Vos Post, Aug 16 2006
EXTENSIONS
Corrected and extended by R. J. Mathar, Dec 16 2006
STATUS
approved