Wednesday, July 18, 2018

[sreubrxp] Multiple highest factor

Numbers which are not a perfect power of a prime, and whose largest prime factor has exponent greater than 1.  One can normally omit the largest factor when giving a prime factorization of a number, but here it is not clear what that means.

f(x)=local(m,s);m=factorint(x);s=matsize(m);if(s[1]==1,0,if(m[s[1],2]==1,0,1))

18 36 50 54 72 75 98 100 108 144 147 150 162 196 200 216 225 242 245 250 288 294 300 324 338 363 375 392 400 432 441 450 484 486 490 500 507 576 578 588 600 605 648 675 676 686 722 726 735 750 784 800 845 847 864 867 882 900 968 972 980 1000 1014 1029 1058 1083 1089 1125 1152 1156 1176 1183 1200 1210 1225 1250 1296 1323 1350 1352 1372 1444 1445 1452 1458 1470 1500 1521 1568 1587 1600 1682 1690 1694 1715 1728 1734 1764 1800 1805 1815 1859 1875 1922 1936 1944 1960 2000 2023 2025 2028 2058 2116 2166 2178 2205 2250 2304 2312 2352 2366 2400 2420 2450 2500 2523 2527 2535 2541 2592 2601 2645 2646 2662 2700 2704 2738 2744 2883 2888 2890 2904 2916 2940 3000 3025 3042 3087 3136 3174 3179 3200 3249 3267 3362 3364 3375 3380 3388 3430 3456 3468 3528 3549 3600 3610 3630 3675 3698 3703 3718 3750 3757 3844 3872 3888 3920 3969 3971 3993 4000 4046 4050 4056 4107 4116 4205 4225 4232 4235 4332 4335 4356 4374 4394 4410 4418 4500 4563 4608 4624 4693 4704 4732 4761 4800 4802 4805 4840 4900 5000 5043 5046 5054 5070 5082 5145 5184 5202 5290 5292 5324 5400 5408 5415 5445 5476 5488 5547 5577 5618 5625 5766 5776 5780 5808 5819 5832 5880 5887 5915 5929 6000 6050 6069 6075 6084 6125 6137 6174 6250 6272 6348 6358 6400 6498 6534 6591 6615 6627 6655 6724 6727 6728 6750 6760 6776 6845 6860 6877 6912 6936 6962 7056 7098 7200 7203 7220 7225 7260 7350 7396 7406 7436 7442 7500 7514 7569 7581 7605 7623 7688 7744 7776 7803 7840 7935 7938 7942 7986 8000 8092 8100 8112 8214 8232 8281 8405 8410 8427 8450 8464 8470 8575 8649 8664 8670 8712 8748 8788 8820 8836 8978 8993 9000 9025 9075 9126 9216 9245 9248 9251 9261 9295 9317 9375 9386 9408 9464 9522 9537 9583 9600 9604 9610 9680 9747 9800 9801 9826 10000

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