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A114380
Largest prime power that divides any number between (exclusive) prime(n) and prime(n+1).
1
4, 3, 9, 4, 16, 9, 11, 27, 5, 32, 19, 7, 23, 49, 29, 5, 64, 23, 9, 37, 81, 43, 47, 49, 17, 53, 27, 37, 125, 128, 67, 23, 73, 25, 31, 81, 83, 169, 89, 9, 61, 64, 97, 11, 103, 109, 113, 19, 29, 79, 16, 243, 256, 131, 89, 27, 137, 139, 47, 289
OFFSET
2,1
LINKS
EXAMPLE
a(4) = 9 because, of the numbers between 7 (= prime(4)) and 11-1 (= prime(5)-1), 9 has the largest prime-power divisor (namely, itself).
a(13) = 7 because only 42 lies between 41 (= prime(13)) and 43 (= prime(14)) and its largest prime-power divisor is 7.
MATHEMATICA
f[n_] := Max[Power @@@ FactorInteger[n]]; g[s_] := Max[Map[f, Range[First[s] + 1, Last[s] - 1]]]; g /@ Partition[Prime[Range[2, 100]], 2, 1] (* Amiram Eldar, May 25 2024 *)
PROG
(PARI) a(n) = {ppmax = 1; for (i = prime(n)+1, prime(n+1)-1, f = factor(i); for (j = 1, #f~, ppmax = max(ppmax, f[j, 1]^f[j, 2]); ); ); ppmax; } \\ Michel Marcus, Aug 25 2013
CROSSREFS
Cf. A246655.
Sequence in context: A074123 A016704 A131896 * A293130 A103825 A073238
KEYWORD
easy,nonn
AUTHOR
Greg Huber, Feb 10 2006
EXTENSIONS
More terms from Joseph Pedersen (jmp456(AT)psu.edu), Apr 27 2006
STATUS
approved