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A236386 Numbers m such that phi(m) is an oblong number.

%I A236386 #27 Mar 03 2023 06:34:10
%S A236386 3,4,6,7,9,13,14,18,21,25,26,28,31,33,36,42,43,44,49,50,62,66,73,86,
%T A236386 87,91,95,98,111,116,117,121,135,146,148,152,157,161,169,174,182,190,
%U A236386 201,207,211,216,222,228,234,237,241,242,252,268,270,287,289,305
%N A236386 Numbers m such that phi(m) is an oblong number.
%C A236386 An oblong number (A002378) is of the form k*(k+1) where k is a natural number.
%C A236386 From _Bernard Schott_, Feb 27 2023: (Start)
%C A236386 Subsequence of primes is A002383 because in this case phi(k^2+k+1) = k*(k+1).
%C A236386 Subsequence of oblong numbers is A359847 where k and phi(k) are both oblong numbers. (End)
%H A236386 Giovanni Resta, <a href="/A236386/b236386.txt">Table of n, a(n) for n = 1..10000</a>
%e A236386 phi(13) = 12 = 3*4, an oblong number; so 13 is a term of the sequence.
%p A236386 filter := m -> issqr(1 + 4*phi(m)) : select(filter, [$(1 .. 700)]); # _Bernard Schott_, Feb 26 2023
%t A236386 Select[Range[500], IntegerQ@Sqrt[1 + 4*EulerPhi[#]] &] (* _Giovanni Resta_, Jan 24 2014 *)
%o A236386 (PARI) isok(m) = my(t=eulerphi(m)); !(t%2) && ispolygonal(t/2, 3); \\ _Michel Marcus_, Feb 27 2023
%o A236386 (Python)
%o A236386 from itertools import count, islice
%o A236386 from sympy.ntheory.primetest import is_square
%o A236386 from sympy import totient
%o A236386 def A236386_gen(startvalue=1): # generator of terms >= startvalue
%o A236386     return filter(lambda n:is_square((totient(n)<<2)+1), count(max(1,startvalue)))
%o A236386 A236386_list = list(islice(A236386_gen(),20)) # _Chai Wah Wu_, Feb 28 2023
%Y A236386 Cf. A000010, A002378, A002383, A359847.
%Y A236386 Similar, but where phi(m) is: A039770 (square), A039771 (cube), A078164 (biquadrate), A096503 (repdigit), A117296 (palindrome), A360944 (triangular).
%K A236386 nonn,easy
%O A236386 1,1
%A A236386 _Joseph L. Pe_, Jan 24 2014
%E A236386 a(16)-a(58) from _Giovanni Resta_, Jan 24 2014