A230357 -id:A230357 - cp's OEIS frontend

A230354 Even numbers n such that digit sum of n = digit sum of largest odd divisor of n.

12, 18, 36, 54, 60, 72, 90, 108, 126, 132, 144, 156, 162, 180, 198, 204, 216, 228, 234, 240, 252, 270, 276, 306, 320, 324, 342, 348, 360, 372, 378, 396, 414, 420, 432, 450, 504, 516, 522, 540, 558, 594, 612, 624, 630, 636, 660, 702, 708, 720, 732, 738, 756, 774, 780, 792, 810, 900

Offset: 1

Antonio Roldán, Oct 16 2013

			Largest odd divisor of 162 is 81. Digit_sum(162)=9, digit_sum(81)=9

Cf. A006753, A219340, A230355, A230356, A230357.

mdi(n)= n / 2^valuation(n, 2)
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=mdi(n);if(digsum(n)==digsum(mdi(n))&&m<>n,print(n)));}

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

Original entry on oeis.org

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)));}

cp's OEIS Frontend

A230354 Even numbers n such that digit sum of n = digit sum of largest odd divisor of n.

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

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PARI

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

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PARI