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A217690 Numbers n such that sum of digits of n equals the least prime dividing n and sum of squares of digits of n equals the greatest prime dividing n. 0

%I #11 Oct 19 2012 13:02:33

%S 133,803,2023,106811,383177,1071949,1342027,2025343,2569757,2911123,

%T 3341831,3993883,6285901,10860071,11194319,13270013,21736109,21871477,

%U 22159451,22421587,26011229,27600257,31174391,32656681,34880611,40435193,41755573,53738911

%N Numbers n such that sum of digits of n equals the least prime dividing n and sum of squares of digits of n equals the greatest prime dividing n.

%F k such that A020639(k) = A007953(k) and A006530(k) = A003132(k).

%e 383177 = 29 * 73 * 181 is in the sequence because 29 = 3+8+3+1+7+7 and 181 = 3^2+8^2+3^2+1^2+7^2+7^2.

%p with(numtheory):A:= proc(n) add(u, u=convert(n, base, 10)) ; end proc: B:= proc(m) add(v^2, v=convert(m, base, 10)) ; end proc: for i from 2 to 1000000 do:x:=factorset(i):n1:=nops(x):if x[1]=A(i) and x[n1]=B(i) then print(i):else fi:od:

%o (PARI) is_A217690(n)={my(d=digits(n),s=norml2(d),f); (n%s || !isprime(s) || n%(d=sum(i=1,#d,d[i])) || !isprime(d)) & return; !(f=factor(n/(d*s))[,1]) || (d <= f[1] & s >= f[#f])} \\ _Charles R Greathouse IV_ and _M. F. Hasler_, Oct 11 2012

%Y Cf. A007953, A003132, A020639, A006530.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Oct 11 2012

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)