A073087 Least k such that sigma(k^k)>=n*k^k.

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

Links

Table of n, a(n) for n=1..9.

David W. Wilson, Comments on this sequence

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: A054721 A074111 A231209 * A214822 A295497 A298457

Adjacent sequences: A073084 A073085 A073086 * A073088 A073089 A073090

Keyword

nonn

Author

Benoit Cloitre, Aug 18 2002

Extensions

More terms from David W. Wilson, Sep 15 2005

Status

approved