A230354 -id:A230354 - cp's OEIS frontend

A230355 Nonsquarefree numbers n such that digit sum of n = digit sum of squarefree part of n.

12, 24, 60, 100, 120, 132, 150, 156, 200, 204, 228, 240, 264, 276, 300, 320, 348, 372, 420, 500, 516, 552, 600, 624, 636, 660, 700, 708, 732, 744, 780, 912, 1000, 1014, 1050, 1056, 1068, 1092, 1100, 1128, 1164, 1200, 1212, 1216, 1236, 1248, 1272, 1300, 1308, 1320, 1356, 1380, 1392, 1400

Offset: 1

Antonio Roldán, Oct 16 2013

			Squarefree part of 624=2^4*3*13 is 39. Digit_sum(624)=12, digit_sum(39)=12

Cf. A006753, A230354, A230356, A230357.

digsum(n)={local (d, p); d=0; p=n; while(p, d+=p%10; p=floor(p/10)); return(d)}
{for (n=4, 10^3,m=core(n);if(digsum(n)==digsum(m)&&m<>n,print(n)));}

A230356 Nonsquare numbers n such that digit sum of n = digit sum of square part of n.

Original entry on oeis.org

10, 18, 27, 40, 45, 54, 63, 72, 90, 108, 117, 126, 135, 153, 160, 162, 171, 180, 207, 216, 220, 234, 243, 250, 252, 261, 270, 304, 306, 315, 333, 342, 351, 360, 405, 414, 423, 432, 450, 490, 504, 513, 522, 531, 540, 603, 612, 621, 630, 640, 702, 711, 720, 801, 810, 931

Offset: 1

Antonio Roldán, Oct 16 2013

			135 = 2^3*5. Square part of 135 is 9. Digit_sum(135) =9, digit_sum(9) = 9.

Cf. A006753, A230354, A230355, A230357.

digsum(n)={local (d, p); d=0; p=n; while(p, d+=p%10; p=floor(p/10)); return(d)}
{for (n=2, 10^3,m=n/core(n);if(digsum(n)==digsum(m)&&m<>n,print(n)));}

A230357 Numbers n such that digit sum of n equals digit sum of sopf(n) (sum of the distinct prime factors of n).

Original entry on oeis.org

22, 94, 105, 114, 136, 140, 160, 166, 202, 222, 234, 250, 265, 274, 346, 355, 361, 382, 424, 438, 445, 454, 516, 517, 526, 532, 562, 634, 702, 706, 712, 732, 812, 913, 915, 922, 1036, 1071, 1086, 1111, 1116, 1122, 1138, 1165, 1185, 1204, 1206, 1219, 1221, 1230, 1239, 1255, 1282, 1312, 1316, 1318, 1345, 1363, 1400, 1404, 1432, 1507, 1520, 1530, 1550

Offset: 1

Antonio Roldán, Oct 16 2013

			166=2*83. Sopf(166)=85. Digit_sum(166)=13, digit_sum(85)=13.

Cf. A006753, A036920, A230354, A230355, A230356.

sopf(n)= { local(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s) }
digsum(n)={local (d, p); d=0; p=n; while(p, d+=p%10; p=floor(p/10)); return(d)}
{for (n=4, 2*10^3,m=sopf(n);if(digsum(n)==digsum(m)&&m<>n,print(n)))}

cp's OEIS Frontend

A230355 Nonsquarefree numbers n such that digit sum of n = digit sum of squarefree part of n.

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A230356 Nonsquare numbers n such that digit sum of n = digit sum of square part of n.

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PARI

A230357 Numbers n such that digit sum of n equals digit sum of sopf(n) (sum of the distinct prime factors of n).

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PARI