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%I #16 Aug 14 2020 06:43:07
%S 12,22,132,34543,612415,27236725,27236752,311162281,311163138,
%T 327361548,9237866583,17499331217,17499551725,36475999489,36475999498
%N Numbers n such that Sum_{d runs through digits of n} d^d = pi(n) (cf. A000720).
%C Note that only two terms, namely 34543 & 17499331217 are primes. So we have: 34543=prime(3^3+4^4+5^5+4^4+3^3), 17499331217=prime(1^1+7^7+4^4+9^9+9^9+3^3+3^3+1^1+2^2+1^1+7^7) and there is no other such prime. - _Farideh Firoozbakht_, Sep 23 2005
%H C. Caldwell and G. L. Honaker, Jr., <a href="https://utm.edu/staff/caldwell/preprints/6521.pdf">Is pi(6521)=6!+5!+2!+1! unique?</a>
%e a(3)=132 because there are exactly 1^1+3^3+2^2 (or 32) prime numbers less than or equal to 132.
%t Do[ If[ Apply[Plus, IntegerDigits[n]^IntegerDigits[n]] == PrimePi[n], Print[n]], {n, 1, 10^7} ]
%Y Cf. A105328, A105329.
%K base,nonn,fini,full
%O 1,1
%A _Jason Earls_, Jan 02 2002
%E More terms from _Robert G. Wilson v_, Jan 15 2002
%E Terms 27236725 onwards from _Farideh Firoozbakht_, Apr 21 2005 and Sep 17 2005
%E Sequence completed by _Farideh Firoozbakht_, Sep 23 2005
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