A324055 Deficiency of Doudna-sequence: a(n) = A033879(A005940(1+n)).

1, 1, 2, 1, 4, 0, 5, 1, 6, 2, 6, -4, 19, -3, 14, 1, 10, 4, 10, -2, 22, -12, 12, -12, 41, 7, 26, -19, 94, -12, 41, 1, 12, 8, 18, 0, 38, -12, 22, -10, 58, -4, 18, -48, 102, -54, 30, -28, 109, 25, 66, -17, 148, -72, 47, -51, 286, 32, 126, -64, 469, -39, 122, 1, 16, 10, 22, 4, 46, -12, 42, -8, 70, 4, 42, -56, 178, -60, 58, -26, 118, 20

Offset

0,3

Comments

Both here and in the mirror image sequence A324185, the lowermost (asinh) scatter plot shows on the y = 0 line the numbers that correspond to the perfect numbers. Compare also to the scatter plot of A243492.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Antti Karttunen, Data supplement: n, a(n) computed for n = 0..70327

Index entries for sequences related to binary expansion of n

Index entries for sequences related to sigma(n)

Formula

a(n) = A033879(A005940(1+n)).

a(n) = 2*A005940(1+n) - A324054(n).

For n > 0, a(n) = A324185(A054429(n)).

a(n) = A324348(n) + A000120(A005940(1+n)).

Mathematica

Array[Block[{p = Partition[Split[Join[IntegerDigits[#, 2], {2}]], 2]}, 2 # - DivisorSigma[1, #] &[Times @@ Flatten@ Table[Prime[Count[Flatten@ #, 0] + 1]^#[[1, 1]] &@ Take[p, -i], {i, Length[p]}]]] &, 82, 0] (* Michael De Vlieger, Mar 11 2019, after Robert G. Wilson v at A005940 *)

Prog

(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A033879(n) = (2*n-sigma(n));
A324055(n) = A033879(A005940(1+n));
(PARI) A324055(n) = { my(m1=2, m2=1, p=2, mp=p*p); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, m1 *= p; if(3==(n%4), mp *= p, m2 *= (mp-1)/(p-1))); n>>=1); (m1-m2); };

Crossrefs

Cf. A000120, A033879, A054429.

See A106737, A290077, A323915, A324052, A324054, A324056, A324057, A324058, A324114, A324335, A324340, A324348, A324349, A324394, A324395 for other sequences as permuted by A005940, and compare their scatter plots.

Cf. also A243492, A323174, A323244, A324185, A324346, A324347, A324654.

Sequence in context: A233905 A285284 A288183 * A087664 A158032 A282886

Adjacent sequences: A324052 A324053 A324054 * A324056 A324057 A324058

Keyword

sign,look

Author

Antti Karttunen, Feb 14 2019

Status

approved