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 A332981 Smallest semiprime m = p*q such that the sum s = p + q can be expressed as an unordered sum of two primes in exactly n ways. 1
 4, 21, 57, 93, 183, 291, 327, 395, 501, 545, 695, 791, 815, 831, 1145, 1205, 1415, 1631, 1461, 1745, 1941, 1865, 2661, 2315, 2615, 2855, 2495, 2285, 3665, 2705, 2721, 3521, 3561, 3351, 3755, 4341, 3545, 4701, 4265, 4881, 3981, 4821, 5601, 5255, 6671, 6041, 4595 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The unique square and even term of the sequence is a(1) = 4. For n = 1, the sequence of semiprimes having an unique decomposition as the sum of two primes begins with 4, 6, 9, 10, 14, 15, 22, 26, 34, 35, 38, 46, 58, 62, ... containing the even semiprimes (A100484). We observe a majority of terms where a(n) == 5 (mod 10). LINKS Michel Marcus, Table of n, a(n) for n = 1..501 EXAMPLE a(11) = 695 because 695 = 5*139 and the sum 5 + 139 = 144 = 5+139 = 7+137 = 13+131 = 17+127 = 31+113 = 37+107 = 41+103 = 43+101 = 47+97 = 61+83 = 71+73. There are exactly 11 decompositions of 144 into an unordered sum of two primes. MAPLE with(numtheory): for n from 1 to 50 do: ii:=0: for k from 2 to 10^8 while(ii=0) do: x:=factorset(k):it:=0: if bigomega(k) = 2   then    s:=x+k/x:     for m from 1 to s/2 do:      if isprime(m) and isprime(s-m)       then        it:=it+1:        else fi:      od:      if it = n      then       ii:=1: printf(`%d, `, k):      else fi:      fi:     od:     od: PROG (PARI) nbp(k) = {my(nb = 0); forprime(p=2, k\2, if (isprime(k-p), nb++); ); nb; } a(n) = {forcomposite(k=1, oo, if (bigomega(k)==2, my(x=factor(k)[1, 1]); if (nbp(x+k/x)==n, return(k)); ); ); } \\ Michel Marcus, Apr 26 2020 CROSSREFS Cf. A001358, A002375, A006881, A023036, A100484, A136244. Sequence in context: A201446 A220772 A242135 * A135559 A254449 A131478 Adjacent sequences:  A332978 A332979 A332980 * A332982 A332983 A332984 KEYWORD nonn AUTHOR Michel Lagneau, Mar 05 2020 STATUS approved

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Last modified June 20 13:02 EDT 2021. Contains 345164 sequences. (Running on oeis4.)