A302125 Numbers whose deficiency is a perfect number.

7, 15, 29, 52, 62, 182, 230, 315, 344, 592, 944, 998, 1155, 2012, 2570, 4028, 6710, 15128, 19688, 20264, 30248, 36224, 38252, 40730, 43964, 52088, 90332, 96128, 168116, 195224, 258512, 262112, 451952, 538112, 991904, 1209632, 1237856, 1659128, 2080544, 2085710, 2102272, 2186132

Offset: 1

Author

Robert G. Wilson v and Waldemar Puszkarz, Apr 01 2018

Keywords

• nonn

Comments

Subsequence of deficient numbers (A005100) whose deficiency (A033879) is a member of perfect numbers (A000396).

Examples

			52 is in the sequence since the divisors of 52 are {1, 2, 4, 13, 26 & 52} so d(52) = 98 and 2*52 - 98 = 6, a perfect number.
		

Crossrefs

Cf. A000396 (perfect numbers), A033879 (deficiency), A005100 (deficient numbers), A141548 (subsequence), A301859 (related sequence).

Programs

Mathematica

fQ[n_] := PerfectNumberQ[2n - DivisorSigma[1, n]]; Select[ Range@ 2500000, fQ]

PARI

for(n=1,25*10^5, d=2*n-sigma(n); d>0&&sigma(d)==2*d&&print1(n ","))