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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 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.)