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A377053 Antidiagonal-sums of the absolute value of the array A377051(n,k) = n-th term of k-th differences of powers of primes.

%I A377053 #5 Oct 22 2024 08:00:06
%S A377053 1,3,4,5,6,13,24,45,80,123,174,229,382,1219,3591,8849,19288,37899,
%T A377053 67442,108323,156054,206733,311525,860955,2710374,7111657,17080759,
%U A377053 38884849,85124764,180097856,368321633,726482493,1377039690,2496856437,4306569569,7016267449
%N A377053 Antidiagonal-sums of the absolute value of the array A377051(n,k) = n-th term of k-th differences of powers of primes.
%C A377053 These are the row-sums of the absolute value of the triangle-version of A377051.
%e A377053 The sixth antidiagonal of A377051 is (8, 1, -1, -2, -3, -4, -5), so a(6) = 24.
%t A377053 nn=20;
%t A377053 t=Table[Differences[NestList[NestWhile[#+1&, #+1,!PrimePowerQ[#]&]&,1,2*nn],k],{k,0,nn}];
%t A377053 Total/@Abs[Table[t[[j,i-j+1]],{i,nn},{j,i}]]
%Y A377053 The version for primes is A376681, noncomposites A376684, composites A377035.
%Y A377053 For squarefree numbers we have A377040, nonsquarefree A377048.
%Y A377053 This is the antidiagonal-sums of the absolute value of A377051.
%Y A377053 The signed version is A377052.
%Y A377053 For leaders we have A377054, for primes A007442 or A030016.
%Y A377053 For first zero-positions we have A377055.
%Y A377053 A version for partitions is A377056, cf. A175804, A053445, A281425, A320590.
%Y A377053 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377053 A008578 lists the noncomposites, differences A075526.
%Y A377053 A023893 and A023894 count integer partitions into prime-powers, factorizations A000688.
%Y A377053 Cf. A000961, A025475, A053707, A057820, A069623, A093555, A174965, A246655, A361102, A376340, A376596.
%K A377053 nonn
%O A377053 0,2
%A A377053 _Gus Wiseman_, Oct 22 2024