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 A336839 Denominator of the arithmetic mean of the divisors of A003961(n). 8
 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Also denominator of A336841(n) / A000005(n). All terms are odd because A336932(n) = A007814(A003973(n)) >= A295664(n) for all n. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 Index entries for sequences computed from indices in prime factorization Index entries for sequences related to sigma(n) FORMULA a(n) = denominator(A003973(n)/A000005(n)). a(n) = d(n)/A336856(n) = d(n)/gcd(d(n),A003973(n)) = d(n)/gcd(d(n),A336841(n)), where d(n) is the number of divisors of n, A000005(n). a(n) = A057021(A003961(n)). For all primes p, and e >= 0, a(A000225(e)) = a(p^((2^e) - 1)) = 1. [See A336856] It seems that for all odd primes p, and with the exponents e=5, 11, 17 or 23 (at least these), a(p^e) = 1. It seems that a(27^((2^n)-1)) = A052940(n-1) for all n >= 1. PROG (PARI) A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; A336839(n) = denominator(sigma(A003961(n))/numdiv(n)); CROSSREFS Cf. A000005, A000225, A003961, A003973, A007814, A052940, A057021, A295664, A336840, A336841, A336856, A336931, A336932. Cf. A336918 (positions of 1's), A336919 (of terms > 1). Cf. A336837 and A336838 (numerators). Sequence in context: A061893 A078530 A362302 * A291568 A350559 A365401 Adjacent sequences: A336836 A336837 A336838 * A336840 A336841 A336842 KEYWORD nonn,frac AUTHOR Antti Karttunen, Aug 07 2020 STATUS approved

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Last modified March 3 00:46 EST 2024. Contains 370499 sequences. (Running on oeis4.)