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self-describing n.  and  sphenic n.

First numbers that belong to both sets:

444422, 10123133, 10123331, 10143331, 10153133, 10193331, 10311733, 10311833, 10311933, 10313315, 10313319, 10331231, 10331431, 10331531, 10331731, 10333114, 10333118, 10333119, 12153133, 12153331, 12173133, 12311533, 12311733, 12313317, 12331531, 12331631, 12331731, 12331831, 12331931, 14103133, 14153133, 14173331, 14183331, 14193133, 14311733, 14313315, 14313318, 14331531, 14331631, 14333115, 14333117, 15123331, 15143331, 15163133, 15163331, 15173331, 15183133, 15193133, 15193331, 15311733, 15311933, 15313310, 15313314, 15313317, 15331731, 16123331, 16213223, 16311233, 16311533, 16313314, 16313315, 16331231, 16331431, 16333115, 17103331, 17123331, 17143133, 17153133, 17163331, 17193133, 17233221, 17311433, 17313315, 17322321, 17331431, 17333110, 17333114, 18123133, 18143133, 18193133, 18193331, 18213223, 18311033, 18311433, 18311533, 18311633, 18313310, 18313315, 18331631, 18333114, 18333115, 19173331, 19311533, 19313314, 19313315, 19313318, 19333117, 20203233, 20242042, 21163223, 21213233, 21233218, 21321723, 21322133, 21322310, 21322315, 21322317, 21323321, 21333221, 23103221, 23173221, 23232442, 23321721, 24234223, 24252542, 24264226, 24292942, 24422626, 24422929, 25242542, 25252442, 26242642, 26244226, 26262442, 26422426, 27322733, 27333227, 28282442, 29242942, 29292442, 29322933, 29333229, 31101933, 31103315, 31121033, 31121733, 31123310, 31123315, 31123317, 31141033, 31141533, 31141733, 31141833, 31141933, 31151633, 31151733, 31153314, 31161833, 31171533, 31171933, 31173315, 31181633, 31183315, 31331017, 31331018, 31331019, 31331219, 31331517, 31331519, 31331615, 31331618, 31331710, 31331810, 31331814, 31331819, 31331915, 31331917, 32152321, 32172321, 32182123, 32192321, 32202033, 32211023, 32211523, 32211723, 32211823, 32211923, 32212317, 32212318, 32213321, 32231521, 32231921, 32232110, 32232115, 32232119, 32282833, 33101431, 33101531, 33101731, 33101931, 33103115, 33103118, 33103119, 33121031, 33121531, 33123115, 33141531, 33141631, 33141731, 33143117, 33151031, 33151431, 33151731, 33153114, 33153118, 33153119, 33163114, 33163118, 33173114, 33173115, 33181631, 33183114, 33183115, 33191031, 33191231, 33191531, 33191731, 33193115, 33193117, 33193118, 33311018, 33311215, 33311218, 33311510, 33311514, 33311615, 33311710, 33311714, 33311815, 33311914, 33322121, 33322929, 42242323, 42242626, 42242727, 42262426, 42272427.