cp's OEIS Frontend

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

%I A377052 #5 Oct 22 2024 08:00:10
%S A377052 1,3,4,5,6,13,-6,45,-50,113,-98,73,274,-1159,3563,-8707,19024,-36977,
%T A377052 64582,-98401,121436,-81961,-147383,860871,-2709964,7110655,-17077217,
%U A377052 38873213,-85085216,179965720,-367884935,725051361,-1372311916,2481473639,-4257624155
%N A377052 Antidiagonal-sums of the array A377051(n,k) = n-th term of k-th differences of powers of primes.
%C A377052 These are the row-sums of the triangle-version of A377051.
%e A377052 The sixth antidiagonal of A377051 is (8, 1, -1, -2, -3, -4, -5), so a(6) = -6.
%t A377052 nn=20;
%t A377052 t=Table[Differences[NestList[NestWhile[#+1&, #+1,!PrimePowerQ[#]&]&,1,2*nn],k],{k,0,nn}];
%t A377052 Total/@Table[t[[j,i-j+1]],{i,nn},{j,i}]
%Y A377052 The version for primes is A140119, noncomposites A376683, composites A377034.
%Y A377052 For squarefree numbers we have A377039, nonsquarefree A377047.
%Y A377052 These are the antidiagonal-sums of A377051.
%Y A377052 The unsigned version is A377053.
%Y A377052 For leaders we have A377054, for primes A007442 or A030016.
%Y A377052 For first zero-positions we have A377055.
%Y A377052 A version for partitions is A377056, cf. A175804, A053445, A281425, A320590.
%Y A377052 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377052 A001597 lists perfect-powers, complement A007916.
%Y A377052 A023893 and A023894 count integer partitions into prime-powers, factorizations A000688.
%Y A377052 Cf. A000961, A025475, A053707, A057820, A093555, A174965, A246655, A361102, A376340, A376596, A376598.
%K A377052 sign
%O A377052 0,2
%A A377052 _Gus Wiseman_, Oct 22 2024