id:A143811 - OEIS Search Results

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Number of numbers k<p such that k^(p-1)-1 is divisible by p^2, p = prime(n).

+0
1

1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2, 3, 3, 2, 1, 1, 2, 1, 3, 1, 1, 1, 2, 2, 1, 2, 2, 3, 2, 1, 3, 2, 1, 2, 1, 2, 2, 4, 1, 1, 2, 2, 2, 2, 1, 3, 1, 4, 1, 3, 3, 3, 3, 3, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 3, 1, 1, 5, 1, 2, 1, 3, 2, 2, 1, 2, 2, 2, 1, 4 (list; graph; listen)

	OFFSET	`1,5`
	COMMENT	`Note that a(n)>0 because k=1 is always a solution. The primes for which a(n)>1 are given in A134307. The values of k are the terms <p in row n of A143548. The largest known terms in this sequence are for the Wieferich primes 1093 and 3511, for which we have a(183)=11 and a(490)=12, respectively. It is not hard to show that k=p-1 is never a solution for odd prime p. In fact, (p-1)^(p-1)=p+1 (mod p^2) for odd prime p.`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..10000`
	MATHEMATICA	`Table[p=Prime[n]; s=Select[Range[p-1], PowerMod[ #, p-1, p^2]==1&]; Length[s], {n, 100}]`
	CROSSREFS	`Sequence in context: A030393 A109393 A030348 this_sequence A109673 A023591 A165661` `Adjacent sequences: A143808 A143809 A143810 this_sequence A143812 A143813 A143814`
	KEYWORD	`nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Sep 02 2008`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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