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

1, 3, 4, 5, 6, 13, 24, 45, 80, 123, 174, 229, 382, 1219, 3591, 8849, 19288, 37899, 67442, 108323, 156054, 206733, 311525, 860955, 2710374, 7111657, 17080759, 38884849, 85124764, 180097856, 368321633, 726482493, 1377039690, 2496856437, 4306569569, 7016267449

Offset: 0

Author

Gus Wiseman, Oct 22 2024

Keywords

• nonn

Comments

These are the row-sums of the absolute value of the triangle-version of A377051.

Examples

			The sixth antidiagonal of A377051 is (8, 1, -1, -2, -3, -4, -5), so a(6) = 24.
		

Crossrefs

The version for primes is A376681, noncomposites A376684, composites A377035.

For squarefree numbers we have A377040, nonsquarefree A377048.

This is the antidiagonal-sums of the absolute value of A377051.

The signed version is A377052.

For leaders we have A377054, for primes A007442 or A030016.

For first zero-positions we have A377055.

A version for partitions is A377056, cf. A175804, A053445, A281425, A320590.

A000040 lists the primes, differences A001223, seconds A036263.

A008578 lists the noncomposites, differences A075526.

A023893 and A023894 count integer partitions into prime-powers, factorizations A000688.

Cf. A000961, A025475, A053707, A057820, A069623, A093555, A174965, A246655, A361102, A376340, A376596.

Programs

Mathematica

nn=20;
t=Table[Differences[NestList[NestWhile[#+1&, #+1,!PrimePowerQ[#]&]&,1,2*nn],k],{k,0,nn}];
Total/@Abs[Table[t[[j,i-j+1]],{i,nn},{j,i}]]