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A341655 a(n) is the number of divisors of prime(n)^2 - 1. 4
2, 4, 8, 10, 16, 16, 18, 24, 20, 32, 28, 24, 40, 32, 24, 32, 32, 32, 32, 60, 30, 48, 32, 60, 42, 48, 40, 32, 64, 48, 54, 64, 40, 64, 48, 60, 32, 40, 40, 32, 48, 96, 64, 32, 72, 90, 64, 56, 32, 64, 60, 96, 72, 96, 40, 40, 64, 96, 32, 80, 32, 48, 96, 80, 40, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) >= A309906(2) = 32 for n > 21.

LINKS

Table of n, a(n) for n=1..66.

FORMULA

a(n) = A000005(A000040(n)^2 - 1) = A000005(A084920(n)).

EXAMPLE

        p =                factorization

   n  prime(n)  p^2 - 1      of p^2 - 1      a(n)

  --  --------  -------  ------------------  ----

   1      2         3    3                     2

   2      3         8    2^3                   4

   3      5        24    2^3 * 3               8

   4      7        48    2^4 * 3              10

   5     11       120    2^3 * 3 * 5          16

   6     13       168    2^3 * 3 * 7          16

   7     17       288    2^5 * 3^2            18

   8     19       360    2^3 * 3^2 * 5        24

   9     23       528    2^4 * 3 * 11         20

  10     29       840    2^3 * 3 * 5 * 7      32

  11     31       960    2^6 * 3 * 5          28

  12     37      1368    2^3 * 3^2 * 19       24

  13     41      1680    2^4 * 3 * 5 * 7      40

  14     43      1848    2^3 * 3 * 7 * 11     32

  15     47      2208    2^5 * 3 * 23         24

  16     53      2808    2^3 * 3^3 * 13       32

  17     59      3480    2^3 * 3 * 5 * 29     32

  18     61      3720    2^3 * 3 * 5 * 31     32

  19     67      4488    2^3 * 3 * 11 * 17    32

  20     71      5040    2^4 * 3^2 * 5 * 7    60

  21     73      5328    2^4 * 3^2 * 37       30

  22     79      6240    2^5 * 3 * 5 * 13     48

  23     83      6888    2^3 * 3 * 7 * 41     32

  24     89      7920    2^4 * 3^2 * 5 * 11   60

MATHEMATICA

Table[DivisorSigma[0, Prime[n]^2-1], {n, 66}] (* Stefano Spezia, Feb 25 2021 *)

PROG

(PARI) a(n) = numdiv(prime(n)^2-1); \\ Michel Marcus, Feb 25 2021

CROSSREFS

Cf. A000005, A000040, A084920, A309906.

Sequence in context: A102431 A076919 A336659 * A171757 A128106 A125021

Adjacent sequences:  A341652 A341653 A341654 * A341656 A341657 A341658

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Feb 25 2021

STATUS

approved

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Last modified May 16 03:46 EDT 2021. Contains 343937 sequences. (Running on oeis4.)