The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A321258 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = sigma_k(n) - n^k. 5
 0, 0, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 3, 1, 0, 1, 1, 5, 1, 3, 0, 1, 1, 9, 1, 6, 1, 0, 1, 1, 17, 1, 14, 1, 3, 0, 1, 1, 33, 1, 36, 1, 7, 2, 0, 1, 1, 65, 1, 98, 1, 21, 4, 3, 0, 1, 1, 129, 1, 276, 1, 73, 10, 8, 1, 0, 1, 1, 257, 1, 794, 1, 273, 28, 30, 1, 5 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS A(n,k) is the sum of k-th powers of proper divisors of n. LINKS Eric Weisstein's World of Mathematics, Proper divisors FORMULA G.f. of column k: Sum_{j>=1} j^k*x^(2*j)/(1 - x^j). Dirichlet g.f. of column k: zeta(s-k)*(zeta(s) - 1). A(n,k) = 1 if n is prime. EXAMPLE Square array begins:   0,  0,   0,   0,   0,    0,  ...   1,  1,   1,   1,   1,    1,  ...   1,  1,   1,   1,   1,    1,  ...   2,  3,   5,   9,  17,   33,  ...   1,  1,   1,   1,   1,    1,  ...   3,  6,  14,  36,  98,  276,  ... MATHEMATICA Table[Function[k, DivisorSigma[k, n] - n^k][i - n], {i, 0, 12}, {n, 1, i}] // Flatten Table[Function[k, SeriesCoefficient[Sum[j^k x^(2 j)/(1 - x^j), {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten CROSSREFS Columns k=0..5 give A032741, A001065, A067558, A276634, A279363, A279364. Cf. A109974, A285425, A286880, A321259 (diagonal). Sequence in context: A217760 A339218 A263412 * A331510 A319854 A124035 Adjacent sequences:  A321255 A321256 A321257 * A321259 A321260 A321261 KEYWORD nonn,tabl AUTHOR Ilya Gutkovskiy, Nov 01 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 27 16:52 EDT 2021. Contains 346308 sequences. (Running on oeis4.)