A123258 -id:A123258 - cp's OEIS frontend

A094783 Numbers k such that, for all m < k, d_i(k) <= d_i(m) for i=1 to Min(d(k),d(m)), where d_i(k) denotes the i-th smallest divisor of k.

1, 2, 4, 6, 12, 24, 48, 60, 120, 240, 360, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 720720, 1441440, 2162160, 3603600, 7207200, 10810800, 122522400, 183783600, 2327925600, 3491888400, 80313433200

Offset: 1

Matthew Vandermast, Jun 10 2004

nonn

The function d(k) (A000005) is the number of divisors of k.
The defining criterion for this sequence is a sufficient, but not necessary, condition for membership in A095849.
Subsequence of A002182. - David Wasserman, Jun 28 2007
Why is 720 not in the sequence? The divisors of 360 begin 1,2,3,4,5,6,8,9,10,12,15,18 (A018412) and the divisors of 720 begin 1,2,3,4,5,6,8,9,10,12,15,16 (A018609). - J. Lowell, Aug 23 2007 [Answer from Don Reble, Sep 11 2007: 720 is precluded by 420. (1,2,3,4,5,6,7,10,12,14,15,20,21,...) (A018444).]
Conjecture: If k is in this sequence, then so is the smallest number with k divisors. (This conjecture is definitely false for A002182 (k=840) and A019505 (k=240).) - J. Lowell, Jan 24 2008

			As k increases, the positive integer k=6 sets or ties the existing records for smallest first, second and third-smallest divisors (1, 2 and 3), as well as for its fourth-smallest (6). Since no smaller integer has more than three divisors, 6 is a term of this sequence.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau Of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 844.
J. Britton, Perfect Number Analyzer.
Wikipedia, Table of divisors.

Cf. A123258.

ge(va, vb) = {for(i=1, min(#va, #vb), if (va[i] > vb[i], return(0));); return(-1);}
isok(k) = {my(dk = divisors(k)); for (m=1, k-1, my(dm = divisors(m)); if (! ge(dk, dm), return(0));); return(1);} \\ Michel Marcus, Mar 16 2022

More terms from David Wasserman, Jun 28 2007

Definition corrected by Ray Chandler, May 05 2008

cp's OEIS Frontend

A094783 Numbers k such that, for all m < k, d_i(k) <= d_i(m) for i=1 to Min(d(k),d(m)), where d_i(k) denotes the i-th smallest divisor of k.

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