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 A341608 Square array A(n,k) = A341524(A246278(n,k)), read by falling antidiagonals; number of prime factors (with mult.) in the denominator of abundancy index as applied onto prime shift array A246278. 5
 1, 2, 1, 0, 2, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 2, 3, 2, 2, 1, 1, 2, 2, 3, 2, 2, 1, 4, 1, 3, 1, 3, 2, 2, 1, 2, 4, 2, 3, 2, 3, 2, 2, 1, 2, 3, 4, 2, 3, 2, 3, 2, 2, 1, 1, 3, 3, 4, 2, 3, 2, 3, 2, 2, 1, 1, 2, 3, 2, 4, 2, 3, 2, 3, 2, 2, 1, 1, 2, 2, 2, 3, 4, 2, 3, 2, 3, 2, 2, 1, 0, 1, 4, 2, 3, 3, 4, 2, 3, 2, 3, 2, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA A(n,k) = A001222(A341606(n,k))) = A001222(A017666(A246278(n,k))). EXAMPLE The top left corner of the array:    n=  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21   2n=  2  4  6  8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 -----+---------------------------------------------------------------    1 | 1, 2, 0, 3, 1, 1, 1, 4, 2, 2, 1, 1, 1, 0, 1, 5, 1, 4, 1, 2, 1,    2 | 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 2, 1, 2, 2, 5, 2, 4, 1, 4, 2,    3 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 1, 3, 3, 5, 2, 4, 1, 4, 2,    4 | 1, 2, 2, 3,*1, 3, 2, 4,*2,*2, 2, 4, 2, 3,*2, 5, 2,*3, 2,*3, 3,    5 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2,*2, 3, 5, 2, 4, 2, 4, 3,    6 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2,*3, 2, 3, 3, 5, 2, 4, 2, 4, 3,    7 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,    8 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3,*1, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,    9 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,   10 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,   11 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2,*3, 2, 3, 3, 5, 2, 4,*1, 4, 3,   12 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,   13 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,   14 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,   15 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2,*2, 3, 5, 2, 4, 2, 4, 3,   16 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,   17 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,   18 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,   19 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,   20 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,   21 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3, etc. Positions where columns are not monotonic (i.e., with sudden drops) are marked with an asterisk (*). See the example section of A341606 for their further elaboration. PROG (PARI) up_to = 105; A246278sq(row, col) = if(1==row, 2*col, my(f = factor(2*col)); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])+(row-1))); factorback(f)); A017666(n) = denominator(sigma(n)/n); A341608sq(row, col) = bigomega(A017666(A246278sq(row, col))); A341608list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A341608sq(col, (a-(col-1))))); (v); }; v341608 = A341608list(up_to); A341608(n) = v341608[n]; CROSSREFS Cf. A001222, A017666, A341606, A341607, A341628. Sequence A341524 applied to prime shift array A246278. Sequence in context: A258033 A153248 A221179 * A153247 A071432 A194508 Adjacent sequences:  A341605 A341606 A341607 * A341609 A341610 A341611 KEYWORD nonn,tabl AUTHOR Antti Karttunen, Feb 16 2021 STATUS approved

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Last modified April 14 22:47 EDT 2021. Contains 342971 sequences. (Running on oeis4.)