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 A065773 Number of divisors of square of true prime powers arising in A065405. 0
 5, 7, 7, 5, 13, 7, 5, 17, 5, 19, 5, 13, 5, 5, 7, 11, 7, 5, 5, 5, 13, 5, 7, 31, 5, 5, 5, 5, 5, 5, 13, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA a(n) = A000005(A065405(n)^2). If A065405(n) = q^c, a prime-power, then sigma(q^(2c)) = A000203(q^(2c)) = (-1 + q^(2c+1))/(q-1) = (-1 + q^A000005(A065405(n)^2))/(q-1) also a prime, from A065403. EXAMPLE n = 3125, tau(nn) = 11, sigma(nn) = 12207031 = (5^(tau(nn)) - 1)/4 = A065403(16) is also a prime. PROG (PARI) { n=0; for (m=1, 10^9, if (isprime(m), next); x=sigma(m^2); if (isprime(x), a=numdiv(m^2); write("b065773.txt", n++, " ", a); if (n==100, return)) ) } \\ Harry J. Smith, Oct 30 2009 CROSSREFS Cf. A000005, A065405, A000203, A065771, A065772, A025475. Sequence in context: A225155 A011269 A093723 * A114916 A001989 A086056 Adjacent sequences:  A065770 A065771 A065772 * A065774 A065775 A065776 KEYWORD nonn AUTHOR Labos Elemer and Robert G. Wilson v, Nov 19 2001 STATUS approved

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Last modified June 4 16:53 EDT 2020. Contains 334828 sequences. (Running on oeis4.)