A066075 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A066075

Number of solutions x to prime(n) = sigma(x) - 1, where prime(n) is the n-th prime.

1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 2, 3, 1, 1, 5, 1, 2, 3, 3, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 6, 1, 4, 2, 5, 1, 1, 1, 1, 3, 3, 1, 3, 7, 1, 6, 1, 2, 3, 2, 1, 1, 1, 3, 2, 4, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 6, 2, 1, 1, 1, 4, 1, 8, 4, 2, 2, 3, 1, 1, 1, 3, 9, 1, 2, 1, 10, 1, 2, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

prime(n) itself is always the largest solution, but often composite solutions also occur.

If a(n)=1, then the single solution is prime(n).

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

EXAMPLE

n=96, p(96)=503, 503=sigma(x)-1 has 10 solutions together with 503: {204, 220, 224, 246, 284, 286, 334, 415, 451, 503} so a(96)=10.

PROG

(PARI) { for (n=1, 1000, a=1; for (x=1, prime(n) - 1, if (prime(n) == (sigma(x) - 1), a++)); write("b066075.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 10 2009

CROSSREFS

Number of solutions to A000040(n) = A000203(x) - 1.

Cf. A000040, A000203, A058340, A066071, A066072, A066073, A066074, A066075, A066076, A066077, A066080.

Sequence in context: A319841 A336099 A290090 * A359211 A072347 A368684

Adjacent sequences: A066072 A066073 A066074 * A066076 A066077 A066078

KEYWORD

nonn

AUTHOR

Labos Elemer, Dec 03 2001

STATUS

approved