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A340793 Sequence whose partial sums give A000203.

%I A340793 #25 Jan 27 2021 07:51:11
%S A340793 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 A340793 -29,11,-2,16,-26,42,-40,31,-15,6,-6,43,-53,22,-4,34,-48,54,-52,40,-6,
%U A340793 -6,-24,76,-67,36,-21,26,-44,66,-48,48,-40,10,-30,108,-106,34,8
%N A340793 Sequence whose partial sums give A000203.
%C A340793 Essentially a duplicate of A053222.
%C A340793 Convolved with the nonzero terms of A000217 gives A175254, the volume of the stepped pyramid described in A245092.
%C A340793 Convolved with the nonzero terms of A046092 gives A244050, the volume of the stepped pyramid described in A244050.
%C A340793 Convolved with A000027 gives A024916.
%C A340793 Convolved with A000041 gives A138879.
%C A340793 Convolved with A000070 gives the nonzero terms of A066186.
%C A340793 Convolved with the nonzero terms of A002088 gives A086733.
%C A340793 Convolved with A014153 gives A182738.
%C A340793 Convolved with A024916 gives A000385.
%C A340793 Convolved with A036469 gives the nonzero terms of A277029.
%C A340793 Convolved with A091360 gives A276432.
%C A340793 Convolved with A143128 gives the nonzero terms of A000441.
%C A340793 For the correspondence between divisors and partitions see A336811.
%F A340793 a(n) = A053222(n-1) for n>1. - _Michel Marcus_, Jan 22 2021
%p A340793 a:= n-> (s-> s(n)-s(n-1))(numtheory[sigma]):
%p A340793 seq(a(n), n=1..77);  # _Alois P. Heinz_, Jan 21 2021
%t A340793 Join[{1}, Differences @ Table[DivisorSigma[1, n], {n, 1, 100}]] (* _Amiram Eldar_, Jan 21 2021 *)
%o A340793 (PARI) a(n) = if (n==1, 1, sigma(n)-sigma(n-1)); \\ _Michel Marcus_, Jan 22 2021
%Y A340793 1 together with A053222.
%Y A340793 Cf. A000203 (partial sums).
%Y A340793 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 A340793 sign,easy
%O A340793 1,2
%A A340793 _Omar E. Pol_, Jan 21 2021