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A073087
Least k such that sigma(k^k)>=n*k^k.
2
1, 6, 30, 210, 30030, 223092870, 13082761331670030, 3217644767340672907899084554130, 1492182350939279320058875736615841068547583863326864530410
OFFSET
1,2
COMMENTS
Does a(n) = the product of primes less than or equal to prime(n+1) = A002110(n+1)? Answer from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Sep 14 2005: No, this is not true.
Note that sigma(k^k) = prod (p^(k r + 1) - 1)/(p - 1). - Mitch Harris, Sep 14 2005
I have proved to my own satisfaction that for n >= 4, A073087(n) = p#, where p is the smallest prime satisfying p#/phi(p#) >= n. See link. - David W. Wilson, Sep 14 2005
FORMULA
a(n) = A091440(n)# = A002110(A112873(n)) for n >= 4.
PROG
(PARI) a(n)=if(n<0, 0, s=1; while(sigma(s^s)<n*s^s, s++); s)
CROSSREFS
Cf. A023199.
Sequence in context: A374660 A074111 A231209 * A214822 A295497 A298457
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Aug 18 2002
EXTENSIONS
More terms from David W. Wilson, Sep 15 2005
STATUS
approved