A377052 Antidiagonal-sums of the array A377051(n,k) = n-th term of k-th differences of powers of primes.

1, 3, 4, 5, 6, 13, -6, 45, -50, 113, -98, 73, 274, -1159, 3563, -8707, 19024, -36977, 64582, -98401, 121436, -81961, -147383, 860871, -2709964, 7110655, -17077217, 38873213, -85085216, 179965720, -367884935, 725051361, -1372311916, 2481473639, -4257624155

Offset: 0

Author

Gus Wiseman, Oct 22 2024

Keywords

• sign

Comments

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

Examples

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

Crossrefs

The version for primes is A140119, noncomposites A376683, composites A377034.

For squarefree numbers we have A377039, nonsquarefree A377047.

These are the antidiagonal-sums of A377051.

The unsigned version is A377053.

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.

A001597 lists perfect-powers, complement A007916.

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

Cf. A000961, A025475, A053707, A057820, A093555, A174965, A246655, A361102, A376340, A376596, A376598.

Programs

Mathematica

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