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 A189394 Highly composite numbers whose number of divisors is also highly composite. 4
 1, 2, 6, 12, 60, 360, 1260, 2520, 5040, 55440, 277200, 720720, 3603600, 61261200, 2205403200, 293318625600, 6746328388800, 195643523275200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Both n and d(n) are highly composite numbers. It is extremely likely that this sequence is complete. The highly composite numbers have a very special form. The number of divisors of a large HCN has a high power of 2 in its factorization -- which is not the form of an HCN. - T. D. Noe, Apr 21 2011 All but a(7) and a(12) are a multiple of the previous term: ratios a(n+1) / a(n) are (2, 3, 2, 5, 6, 7/2, 2, 2, 11, 5, 13/5, 5, 17, 36, 133, 23, 29, ...?). - M. F. Hasler, Jun 20 2022 LINKS Table of n, a(n) for n=1..18. Achim Flammenkamp, Highly composite numbers Lars Magnus Øverlier, Highly Composite Numbers, arXiv:2305.14350 [math.NT], 2023. EXAMPLE d(60) = 12; both 60 and 12 are highly composite numbers MATHEMATICA (* First run program at A002182 *) Select[A002182, MemberQ[A002182, DivisorSigma[0, #]] &] (* Alonso del Arte, Apr 21 2011 *) PROG (PARI) is_A189394(n)={is_A002182(numdiv(n)) && is_A002182(n)} M189394=[1, 2]/*for memoization*/; A189394(n)={if(#M189394

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Last modified December 2 06:06 EST 2023. Contains 367508 sequences. (Running on oeis4.)