A181471 - OEIS

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A181471

a(n) = number of numbers of the form k^2-1 having n-th prime as largest prime divisor.

1, 4, 8, 16, 20, 34, 47, 72, 95, 126, 168, 208, 262, 343, 433, 507, 634, 799, 976, 1146, 1439, 1698, 2082, 2371, 2734

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OFFSET

1,2

COMMENTS

Theorem: zero does not occur in this sequence. Proof: (p-1)^2-1=(p-2)p. This means that p is greatest prime divisor of (p-1)^2-1 for every p.

a(2)-a(25)=total number of terms in A181447-A181470.

An effective abc conjecture (c < rad(abc)^2) would imply that a(24)-a(33) are (2371, 2734, 3360, 4022, 4637, 5575, 6424, 7268, 8351, 9661). - Lucas A. Brown, Oct 01 2022

LINKS

Table of n, a(n) for n=1..25.

Wikipedia, Størmer's theorem

CROSSREFS

Cf. A175607, A175901-A175904, A181447-A181470.

Sequence in context: A312805 A312806 A036693 * A272753 A272804 A237990

Adjacent sequences: A181468 A181469 A181470 * A181472 A181473 A181474

KEYWORD

nonn,hard,more

AUTHOR

Artur Jasinski, Oct 21-22 2010

EXTENSIONS

Wrong terms a(24)-a(25) removed by Lucas A. Brown, Oct 01 2022

a(24)-a(25) from David A. Corneth, Oct 01 2022

STATUS

approved