A101259 Numbers whose deficiency is 54.

87, 195, 244, 495, 11584, 35595, 137452847104, 9007202811510784, 590295811269238718464, 38685626227901230055686144

Offset

1,1

Comments

Contains numbers 2^(k-1)*(2^k + 53) whenever 2^k + 53 is prime. - Max Alekseyev, Oct 17 2025

a(11) <= 2^74 * (2^75 + 53) = 713623846352979940530144126419115932976676864. - Max Alekseyev, Mar 04 2026

Links

Table of n, a(n) for n=1..10.

Example

87 is a term of the sequence because 3*29 = 87 and 87 - 29 - 3 = g(87) = 55.

Mathematica

Do[ If[ DivisorSigma[1, n] + 54 == 2n, Print[n]], {n, 10^7}] (* Robert G. Wilson v, Dec 22 2004 *)

Prog

(Magma) [n: n in [1..2*10^7] | DivisorSigma(1, n)+54 eq 2*n]; // Vincenzo Librandi, Jul 30 2015

Crossrefs

Deficiency k: A191363 (k=2), A125246 (k=4), A141548 (k=6), A125247 (k=8), A101223 (k=10), A141549 (k=12), A141550 (k=14), A125248 (k=16), A223608 (k=18), A223607 (k=20), A223606 (k=22), A385255 (k=24), A275702 (k=26), A387352 (k=32), A175730 (k=42), A275997 (k=64).

Abundance k: A088831 (k=2), A088832 (k=4), A087167 (k=6), A088833 (k=8), A223609 (k=10), A141545 (k=12), A141546 (k=14), A141547 (k=16), A223610 (k=18), A223611 (k=20), A223612 (k=22), A223613 (k=24), A275701 (k=26), A175989 (k=32), A275996 (k=64), A292626 (k=128).

Cf. A033879.

Sequence in context: A044800 A067749 A063349 * A063336 A129515 A133524

Adjacent sequences: A101256 A101257 A101258 * A101260 A101261 A101262

Keyword

nonn,more

Author

Vassil K. Tintschev (tinchev(AT)sunhe.jinr.ru), Dec 17 2004

Extensions

a(7) from Donovan Johnson, Dec 23 2008

a(8)-a(9) from Max Alekseyev, Oct 17 2025

a(10) from Max Alekseyev, Mar 04 2026

Status

approved