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A131457 Higgs' semiprimes: a(n+1) = next semiprime such that a(n+1)-1 | (a(1)...a(n))^2. 1
4, 9, 10, 21, 22, 25, 26, 33, 34, 35, 46, 49, 51, 55, 57, 58, 65, 69, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 161, 166, 169, 177, 178, 183, 185, 187, 201, 202, 203, 205, 206, 209, 213 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is to semiprimes A001358 as A007459 is to primes A000040. Finite or infinite?

LINKS

Table of n, a(n) for n=1..59.

FORMULA

a(n+1) = MIN{j in A001358 such that (j-1) | PRODUCT[i=1..n]a(i)^2.

EXAMPLE

a(1) = 4 because 4 = 2^2 is the first semiprime.

a(2) = 9 because 9 = 3^2 is the next semiprime after 4, where 9-1=8 divides 4^2 = 16.

a(3) = 10 because 10 = 2*5 is the next semiprime after 9 where 10-9=9 divides (4*9)^2.

a(4) = 21 because 21 = 3*7 is the next semiprime after 10, where 10-1=9 divides (4*9*10)^2.

a(5) = 22 because 22 = 2*11 is the next semiprime after 21, where 21-1=20 divides (4*9*10*21)^2.

MAPLE

isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true ; else false; fi ; end: A131457 := proc(n) option remember ; local a, prevpr; if n =1 then 4; else prevpr := (mul(A131457(i), i=1..n-1))^2 ; a := A131457(n-1)+1 ; while not isA001358(a) or prevpr mod (a-1) <> 0 do a := a+1 ; od; RETURN(a) ; fi ; end: seq(A131457(n), n=1..80) ; # R. J. Mathar, Oct 30 2007

CROSSREFS

Cf. A000040, A001358, A007459, A070552, A109373.

Sequence in context: A263648 A051884 A131368 * A072525 A338906 A107621

Adjacent sequences:  A131454 A131455 A131456 * A131458 A131459 A131460

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Oct 21 2007

EXTENSIONS

Corrected and extended by R. J. Mathar, Oct 30 2007

STATUS

approved

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Last modified June 28 15:11 EDT 2022. Contains 354907 sequences. (Running on oeis4.)