A153428 -id:A153428 - cp's OEIS frontend

A153427 Numbers n such that phi(n)=p^2, where p is product of digits of n.

1, 12, 125, 451, 4612, 5412, 8313, 22165, 31815, 34125, 43216, 62232, 111398, 115264, 115625, 126225, 142352, 191425, 194313, 235431, 243135, 261532, 265421, 632613, 726313, 852125, 962312, 1142536, 1148316, 1156324, 1162825, 1183491, 1671183, 1672125, 1815912, 1831525, 1914157, 2124535, 2228224, 2321375, 2364132, 2463312, 3356122, 3416541, 3541252, 3716118, 3741812, 4128831, 4218912, 4331236, 4522136, 5148512, 5181293, 5183219, 5463161, 6219612, 6288113, 6411925, 6811922, 7452313, 7518119, 8741341, 9115625, 9324222

Offset: 1

Farideh Firoozbakht, Jan 02 2009

			phi(2228224)=(2*2*2*8*2*2*4)^2, so 2228224 is in the sequence.

Max Alekseyev, Table of n, a(n) for n = 1..649

Cf. A068572, A153428.

Do[If[Apply[Times,IntegerDigits[n]]^2==EulerPhi[n],Print[n]],{n,1200000}]
Select[Range[94*10^5],EulerPhi[#]==(Times@@IntegerDigits[#])^2&] (* Harvey P. Dale, May 03 2020 *)

a(33)-a(649) from Max Alekseyev, Aug 18 2013, May 31 2018

A171267 Primes p such that p^s ends with p, where s is sum of the digits of p.

Original entry on oeis.org

5, 29, 193, 557, 751, 3307, 4999, 7499, 16693, 20807, 31249, 59999, 60443, 79193, 812501, 918751, 5422943, 46295807, 55781249, 74218751, 78281249, 89218751, 89999999, 282922943, 316295807, 674218751, 1583704193, 3824218751, 3958704193, 4092077057, 6342077057, 8324218751, 31666295807, 47779577057, 64478795807, 66666295807, 75000000001

Offset: 1

Farideh Firoozbakht, Apr 28 2010

			1583704193^(1+5+8+3+7+0+4+1+9+3)=1583704193 (mod 10^10) so 1583704193 is
in the sequence.
It is interesting that each of the four numbers 751^(7+5+1), 751^(7*5*1),
751^pi(751) and 751^prime(751) ends with 751.

Max Alekseyev, Table of n, a(n) for n = 1..107

Cf. A171268, A153427, A153428.

Do[n=Prime[m];a=IntegerDigits[n];If[PowerMod[n,Apply[Plus,a],10^Length[a]]
==n,Print[n]],{m,100000000}]

Terms a(28) onward from Max Alekseyev, Aug 18 2013

cp's OEIS Frontend

A153427 Numbers n such that phi(n)=p^2, where p is product of digits of n.

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