cp's OEIS Frontend

A294898 Deficiency minus binary weight: a(n) = A033879(n) - A000120(n) = A005187(n) - A000203(n).

%I A294898 #36 Dec 16 2024 13:29:29
%S A294898 0,0,0,0,2,-2,3,0,3,0,7,-6,9,1,2,0,14,-5,15,-4,7,5,18,-14,16,7,10,-3,
%T A294898 24,-16,25,0,16,12,19,-21,33,13,18,-12,37,-15,38,1,8,16,41,-30,38,4,
%U A294898 26,3,48,-16,33,-11,30,22,53,-52,55,23,16,0,44,-14,63,8,39,-7,66,-53,69,31,22,9,54,-16,73,-28,38,35,78,-59,58
%N A294898 Deficiency minus binary weight: a(n) = A033879(n) - A000120(n) = A005187(n) - A000203(n).
%C A294898 "Least deficient numbers" or "almost perfect numbers" are those k for which A033879(k) = 1, or equally, for which a(k) = -A048881(k-1). The only known solutions are powers of 2 (A000079), all present also in A295296. See also A235796 and A378988. - _Antti Karttunen_, Dec 16 2024
%H A294898 Antti Karttunen, <a href="/A294898/b294898.txt">Table of n, a(n) for n = 1..16384</a>
%H A294898 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A294898 a(n) = A005187(n) - A000203(n).
%F A294898 a(n) = A011371(n) - A001065(n).
%F A294898 a(n) = A033879(n) - A000120(n).
%F A294898 Sum_{k=1..n} a(k) ~ c * n^2, where c = 1 - zeta(2)/2 = 0.177532... . - _Amiram Eldar_, Feb 22 2024
%t A294898 Array[IntegerExponent[(2 #)!, 2] - DivisorSigma[1, #] &, 85] (* _Michael De Vlieger_, Nov 26 2017 *)
%o A294898 (Scheme) (define (A294898 n) (- (A005187 n) (A000203 n)))
%o A294898 (PARI) A294898(n) = ((2*n-sigma(n))-hammingweight(n)); \\ _Antti Karttunen_, Dec 16 2024
%Y A294898 Cf. A000120, A000203, A001065, A005187, A011371, A013661, A033879, A048881, A235796, A294896, A294899, A297114 (Möbius transform), A317844 (difference from a(n)), A326133, A326138, A324348 (a(n) applied to Doudna sequence), A379008 (a(n) applied to prime shift array), A378988.
%Y A294898 Cf. A295296 (positions of zeros), A295297 (parity of a(n)).
%K A294898 sign
%O A294898 1,5
%A A294898 _Antti Karttunen_, Nov 25 2017
%E A294898 Name edited by _Antti Karttunen_, Dec 16 2024