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 A323762 Numbers m such that Product_{d|m} (pod(d)/tau(d)) is an integer h where pod(k) = the product of the divisors of k (A007955) and tau(k) = the number of the divisors of k (A000005). 1
 1, 2, 12, 18, 24, 36, 54, 60, 72, 84, 90, 108, 120, 126, 132, 150, 156, 168, 180, 198, 204, 216, 228, 234, 240, 252, 264, 270, 276, 294, 300, 306, 312, 342, 348, 360, 372, 378, 396, 408, 414, 420, 444, 450, 456, 468, 480, 492, 504, 516, 522, 540, 552, 558, 564 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Corresponding values of integers h: 1, 1, 10368, 118098, 6879707136, 101559956668416, ... Product_{d|n} (pod(d)/tau(d)) > 1 for all n > 2. LINKS FORMULA A323761(a(n)) = 1. EXAMPLE 12 is term because Product_{d|12} (pod(d)/tau(d)) = (pod(1)/tau(1))*(pod(2)/tau(2))*(pod(3)/tau(3))*(pod(4)/tau(4)*(pod(6)/tau(6)*(pod(12)/tau(12)) = (1/1)*(2/2)*(3/2)*(8/3)*(36/4)*(1728/6) = 10368 (integer). PROG (MAGMA) [n: n in [1..1000] | Denominator(&*[&*[c: c in Divisors(d)] / NumberOfDivisors(d): d in Divisors(n)]) eq 1] (PARI) isok(n) = my(p=1, vd); fordiv(n, d, vd = divisors(d); p *= vecprod(vd)/#vd); denominator(p) == 1; \\ Michel Marcus, Jan 30 2019 CROSSREFS Cf. A000005, A007955, A323760, A323761. Sequence in context: A144264 A277961 A294998 * A120350 A293851 A032413 Adjacent sequences:  A323759 A323760 A323761 * A323763 A323764 A323765 KEYWORD nonn AUTHOR Jaroslav Krizek, Jan 27 2019 STATUS approved

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Last modified June 15 22:19 EDT 2019. Contains 324145 sequences. (Running on oeis4.)