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A344825 Integers whose digit sum is prime and whose digit product is a perfect square > 0.

%I A344825 #29 May 30 2021 13:01:00
%S A344825 11,14,41,49,94,111,119,122,128,133,155,166,182,188,191,199,212,218,
%T A344825 221,229,236,263,281,289,292,298,313,326,331,362,368,386,449,494,515,
%U A344825 551,559,595,616,623,632,638,661,683,779,797,812,818,821,829,836,863,881
%N A344825 Integers whose digit sum is prime and whose digit product is a perfect square > 0.
%C A344825 If k is in the sequence then all anagrams of k are in the sequence. - _David A. Corneth_, May 29 2021
%C A344825 Trivially, this sequence has infinite elements. A031974 is an infinite sequence that is found in this sequence - _Ryan Bresler_, May 30 2021
%H A344825 David A. Corneth, <a href="/A344825/b344825.txt">Table of n, a(n) for n = 1..10000</a>
%e A344825 11 is a term because its digit sum is 2 (prime) and its digit product is 1 (perfect square > 0).
%p A344825 q:= n-> (l-> not 0 in l and isprime(add(i, i=l)) and
%p A344825          issqr(mul(i, i=l)))(convert(n, base, 10)):
%p A344825 select(q, [$0..999])[];  # _Alois P. Heinz_, May 29 2021
%o A344825 (Python)
%o A344825 from math import prod
%o A344825 from sympy import isprime, integer_nthroot
%o A344825 def ok(n):
%o A344825   d = list(map(int, str(n)))
%o A344825   return 0 not in d and isprime(sum(d)) and integer_nthroot(prod(d), 2)[1]
%o A344825 print(list(filter(ok, range(1000)))) # _Michael S. Branicky_, May 29 2021
%Y A344825 Intersection of A028834 and A050626.
%Y A344825 Subsequence of A052382.
%Y A344825 A031974 is a subsequence of this sequence.
%K A344825 nonn,base
%O A344825 1,1
%A A344825 _Ryan Bresler_, May 29 2021