login
Sequence whose partial sums give A000203.
14

%I #25 Jan 27 2021 07:51:11

%S 1,2,1,3,-1,6,-4,7,-2,5,-6,16,-14,10,0,7,-13,21,-19,22,-10,4,-12,36,

%T -29,11,-2,16,-26,42,-40,31,-15,6,-6,43,-53,22,-4,34,-48,54,-52,40,-6,

%U -6,-24,76,-67,36,-21,26,-44,66,-48,48,-40,10,-30,108,-106,34,8

%N Sequence whose partial sums give A000203.

%C Essentially a duplicate of A053222.

%C Convolved with the nonzero terms of A000217 gives A175254, the volume of the stepped pyramid described in A245092.

%C Convolved with the nonzero terms of A046092 gives A244050, the volume of the stepped pyramid described in A244050.

%C Convolved with A000027 gives A024916.

%C Convolved with A000041 gives A138879.

%C Convolved with A000070 gives the nonzero terms of A066186.

%C Convolved with the nonzero terms of A002088 gives A086733.

%C Convolved with A014153 gives A182738.

%C Convolved with A024916 gives A000385.

%C Convolved with A036469 gives the nonzero terms of A277029.

%C Convolved with A091360 gives A276432.

%C Convolved with A143128 gives the nonzero terms of A000441.

%C For the correspondence between divisors and partitions see A336811.

%F a(n) = A053222(n-1) for n>1. - _Michel Marcus_, Jan 22 2021

%p a:= n-> (s-> s(n)-s(n-1))(numtheory[sigma]):

%p seq(a(n), n=1..77); # _Alois P. Heinz_, Jan 21 2021

%t Join[{1}, Differences @ Table[DivisorSigma[1, n], {n, 1, 100}]] (* _Amiram Eldar_, Jan 21 2021 *)

%o (PARI) a(n) = if (n==1, 1, sigma(n)-sigma(n-1)); \\ _Michel Marcus_, Jan 22 2021

%Y 1 together with A053222.

%Y Cf. A000203 (partial sums).

%Y Cf. A000027, A000041, A000070, A000217, A000385, A000441, A002088, A002961, A014153, A024916, A036469, A046092, A053223, A053224, A053225, A053226, A053227, A066186, A086733, A091360, A138879, A143128, A175254, A182738, A237593, A244050, A245092, A276432, A277029, A336811.

%K sign,easy

%O 1,2

%A _Omar E. Pol_, Jan 21 2021