A359963 Arithmetic numbers (A003601) having more divisors than all smaller arithmetic numbers.

1, 3, 6, 20, 30, 60, 168, 420, 840, 1980, 2160, 2520, 7560, 10080, 15120, 27720, 79200, 83160, 110880, 166320, 262080, 332640, 554400, 786240, 831600, 1081080, 1441440, 2162160, 2882880, 4324320, 7207200, 8648640, 10810800, 17297280, 21621600, 36756720, 43243200

Offset

1,2

Comments

The corresponding numbers of divisors are 1, 2, 4, 6, 8, 12, 16, 24, 32, ... .

This sequence is infinite since there are arithmetic numbers with any number of divisors (see A359965).

Links

Amiram Eldar, Table of n, a(n) for n = 1..55

Mathematica

seq[nmax_] := Module[{s = {}, dm = 0, d}, Do[d = DivisorSigma[0, n]; If[d > dm && Divisible[DivisorSigma[1, n], d], dm = d; AppendTo[s, n]], {n, 1, nmax}]; s]; seq[10^6]

Prog

(PARI) lista(nmax) = {my(dm = 0, d); for(n = 1, nmax, d = numdiv(n); if(d > dm && sigma(n)%d == 0, dm = d; print1(n, ", "))); }

Crossrefs

Subsequence of A003601.

Cf. A000005, A359965.

Similar sequences: A002182, A335317, A359964.

Sequence in context: A355605 A356912 A176993 * A276748 A339639 A081181

Adjacent sequences: A359960 A359961 A359962 * A359964 A359965 A359966

Keyword

nonn

Author

Amiram Eldar, Jan 20 2023

Status

approved