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Achilles n.  and  nude n.

First numbers that belong to both sets:

288, 432, 648, 864, 1944, 2888, 3888, 6912, 12168, 14112, 18432, 21168, 23328, 24696, 26136, 31212, 34848, 34992, 42336, 49392, 62424, 69192, 69984, 77175, 83232, 84672, 93312, 98784, 111132, 114264, 124416, 124848, 133128, 139392, 139968, 148176, 169344, 172872, 191664, 194688, 199692, 221184, 222264, 228488, 233928, 246924, 249696, 294912, 313632, 314928, 316368, 332928, 333396, 338688, 363312, 383328, 383688, 399384, 426888, 431244, 442368, 484128, 493848, 499392, 636192, 666792, 677376, 691488, 824328, 862488, 914112, 919368, 968832, 969624, 1123632, 1149984, 1161288, 1168128, 1182816, 1213488, 1236492, 1241888, 1292832, 1314144, 1391112, 1414944, 1431432, 1492992, 1633932, 1663488, 1722448, 1778112, 1788696, 1828224, 1866312, 1868184, 1912968, 1939248, 2122416, 2222316, 2239488, 2281248, 2333772, 2384928, 2626632, 2628288, 2661336, 2667168, 2681928, 2696112, 2822688, 2829888, 2988216, 3183624, 3214944, 3232332, 3321216, 3429216, 3483864, 3612672, 3841992, 3942432, 3981312, 4148928, 4173624, 4181832, 4244832, 4294296, 4392648, 4416984, 4428288, 4444632, 4829832, 4942368, 4962312, 6133248, 6181128, 6223392, 6322176, 6324912, 6393888, 6429888, 6464664, 6642432, 6963912, 7112448, 7137144, 7641648, 8347248, 8669448, 8813664, 8821888, 8833968, 8889264, 8964648, 9124992, 9176328, 9383112, 9483264, 9644832, 9891936, 9924624, 9963648, 11197872, 11214848, 11389248, 11462472, 11693448, 11868192, 12122888, 12162312, 12192768, 12266496, 12338136, 12632112, 12649824, 12882888, 12929328, 13127688, 13189248, 13284864, 13333896, 13381632, 13392216, 13395375, 13436928, 13446972, 13686912, 13716864, 13764492, 14129928, 14224896, 14274288, 14386248, 14489496, 16216416, 16313472, 16342632, 16693344, 16694496, 16866432, 16936128, 17784648, 17929296, 18144288, 18216648, 18948168, 19181664, 19319328, 19324332, 19361664, 19393992, 19618848, 19849248, 19996488, 21229128, 21281288, 21337344, 21411432, 21438288, 21482928, 21621888, 21781872, 21938688, 22284488, 22478848, 22498632, 23191344, 23228928, 23238144, 23639688, 23722272, 24114272, 24293412, 24388128, 24822936, 26128368, 26142912, 26249292, 26611416, 26676972, 26893944, 27114248, 27276732, 27433728, 28149336, 28449792, 28619136, 28788872, 28934496, 28978992, 29399112, 31268232, 31648968, 31684824, 32128128, 32183136, 32224392, 32391216, 32432832, 32823144, 32999688, 33146928, 33191424, 33386688, 33388992, 33488928, 33882912, 34319232, 34387416, 34666128, 34843392, 36132696, 36486936, 36499968, 36911232, 38363328, 38466144, 38621232, 38648664.

Some larger examples :