A342833 Integers m such that the number of divisors whose last digit equals the last digit of m sets a new record.

1, 11, 40, 60, 120, 240, 360, 480, 600, 1200, 1800, 2400, 3600, 7200, 8400, 12600, 16800, 25200, 50400, 75600, 100800, 151200, 201600, 252000, 277200, 453600, 504000, 554400, 831600, 1108800, 1663200, 2217600, 2772000, 3326400, 4989600, 5544000, 6652800, 7207200

Offset: 1

Author

Bernard Schott, Mar 23 2021

Keywords

• nonn
• base

Comments

Inspired by Project Euler, Problem 474 (see link).

The corresponding number of divisors whose last digit equals the last digit: 1, 2, 3, 4, 6, 8, 9, 10, 12, 16, 18, 20, ...

Examples

			a(5) = 120 is in the sequence because A330348(120) = 6, the six corresponding divisors are {10, 20, 30, 40, 60, 120} and 6 is larger than any earlier value in A330348.
		

Links

• Project Euler, Problem 474: Last digits of divisors.

Crossrefs

Cf. A002182, A002183, A330348, A335491.

Programs

Mathematica

d[n_] := DivisorSum[n, 1 &, Mod[# - n, 10] == 0 &]; dm = 0; s = {}; Do[d1 = d[n]; If[d1 > dm, dm = d1; AppendTo[s, n]], {n, 1, 10^7}]; s (* Amiram Eldar, Mar 23 2021 *)

PARI

f(n) = my(dig = n%10); sumdiv(n, d, d%10 == dig); \\ A330348
lista(nn) = my(m, k=0, kk); for (n=1, nn, kk = f(n); if (kk>k, print1(n, ", "); k = kk)); \\ Michel Marcus, Mar 24 2021

Formula

For n >= 3, a(n) = 10 * A002182(n) (conjectured).