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

1,1

Comments

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

Links

Table of n, a(n) for n=1..42.

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A274090 A195041 A229462 * A006188 A198589 A298391

Adjacent sequences: A302122 A302123 A302124 * A302126 A302127 A302128

Keyword

nonn

Author

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

Status

approved