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 A066075 Number of solutions x to prime(n) = sigma(x) - 1, where prime(n) is the n-th prime. 11
 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: A305079 A319841 A290090 * A072347 A318831 A303710 Adjacent sequences:  A066072 A066073 A066074 * A066076 A066077 A066078 KEYWORD nonn AUTHOR Labos Elemer, Dec 03 2001 STATUS approved

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Last modified April 23 06:08 EDT 2019. Contains 322381 sequences. (Running on oeis4.)