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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..105.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

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

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.

License Agreements, Terms of Use, Privacy Policy. .

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