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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.
7
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
0,2
COMMENTS
These are the row-sums of the absolute value of the triangle-version of A377051.
EXAMPLE
The sixth antidiagonal of A377051 is (8, 1, -1, -2, -3, -4, -5), so a(6) = 24.
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}]]
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.
Sequence in context: A377052 A070981 A107228 * A355706 A351711 A294247
KEYWORD
nonn,new
AUTHOR
Gus Wiseman, Oct 22 2024
STATUS
approved