A292365 Abundant numbers n such that sigma(sigma(n) - 2*n) = sigma(n).

120, 672, 1740, 7776, 19260, 20640, 21384, 21924, 22428, 25830, 31440, 55968, 93024, 101010, 106140, 143910, 151164, 198792, 246510, 309582, 326196, 411138, 421596, 428256, 499464, 523776, 590112, 639288, 697158, 870552, 941094, 958716, 1060956, 1068210, 1087776, 1100640, 1105884, 1269828

Offset: 1

Author

Altug Alkan, Sep 15 2017

Keywords

• nonn

Comments

A005820 is a subsequence.

101010 is the least squarefree term. For 6 <= k <= 8, the smallest squarefree terms with k prime factors are 101010 = 2*3*5*7*13*37, 35574630 = 2*3*5*7*13*83*157, and 401738610 = 2*3*5*7*13*31*47*101.

Examples

			120 is a term because sigma(sigma(120) - 240) = sigma(360 - 240) = sigma(120).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1210 (terms below 4*10^9)

Crossrefs

Cf. A000203, A005101, A005820.

Programs

Mathematica

Select[Range[1.3*^6], (d = DivisorSigma[1, #]; d > 2 # && DivisorSigma[1, d - 2 #] == d) &] (* Giovanni Resta, Sep 18 2017 *)

PARI

s(n) = sigma(n);
isok(n) = s(n)>2*n && s(s(n)-2*n)==s(n);