A324726 -id:A324726 - cp's OEIS frontend

A324652 Numbers k such that A318468(k) (bitwise-AND of 2k and sigma(k)) is equal to 2k.

6, 12, 18, 20, 24, 28, 36, 40, 48, 56, 80, 88, 96, 100, 104, 112, 160, 176, 192, 196, 200, 204, 208, 220, 224, 260, 264, 272, 304, 320, 336, 352, 368, 384, 392, 416, 448, 464, 496, 544, 550, 580, 608, 640, 648, 650, 672, 704, 736, 768, 784, 832, 896, 928, 992, 1032, 1040, 1044, 1056, 1060, 1068, 1088, 1104, 1120, 1184, 1216

Offset: 1

Antti Karttunen, Mar 14 2019

nonn

Positions of zeros in A324658, fixed points of A324659.
Intersection with A324649 gives A324643.
Intersection with A324726 gives A000396.
In the range 1..2^32 there are only 22 odd terms. See A324647.

Cf. A000203, A191218, A318468, A324647, A324649, A324658, A324659, A324722, A324726.

Some subsequences: A000396, A324643, A324647 (the odd terms).

Select[Range[2000], 2*# == BitAnd[2*#, DivisorSigma[1, #]] &] (* Paolo Xausa, Mar 11 2024 *)

for(n=1,oo,if((n+n)==bitand(2*n,sigma(n)), print1(n, ", ")))

A324727 Odd numbers such that 2n is equal to A318466(n), bitor(2*n,sigma(n)), where bitor is A003986.

Original entry on oeis.org

3, 7, 15, 21, 31, 55, 57, 63, 93, 105, 111, 127, 171, 189, 201, 213, 215, 217, 231, 237, 249, 253, 255, 315, 351, 357, 363, 369, 381, 393, 447, 465, 469, 473, 483, 489, 497, 501, 511, 651, 705, 747, 759, 789, 813, 831, 833, 879, 889, 895, 917, 959, 987, 989, 1001, 1015, 1023, 1155, 1365, 1377, 1407, 1467, 1491, 1503, 1505, 1515, 1533, 1595

Offset: 1

Antti Karttunen, Mar 15 2019

Odd terms of A324726.

Cf. A000203, A003986, A318466, A324647, A324718, A324719.

Select[Range[1, 2000, 2], 2*# == BitOr[2*#, DivisorSigma[1, #]] &] (* Paolo Xausa, Mar 11 2024 *)

for(n=1,oo,if((n%2)&&((2*n)==bitor(2*n,sigma(n))),print1(n,", ")));

A324723 Numbers n such that bitor(2*k, sigma(k)) == 2k, where k = A156552(n).

Original entry on oeis.org

4, 8, 9, 16, 27, 30, 32, 45, 64, 72, 125, 128, 135, 144, 243, 250, 256, 270, 315, 405, 420, 480, 490, 512, 576, 600, 675, 756, 810, 825, 875, 988, 1000, 1024, 1152, 1155, 1210, 1215, 1458, 1470, 1600, 1690, 1716, 1728, 1920, 2048, 2100, 2187, 2250, 2430, 2450, 2475, 3125, 3234, 3240, 3600, 3645, 3825, 4320, 4375, 5070, 5103

Offset: 1

Antti Karttunen, Mar 15 2019

nonn

Cf. A156552, A323243, A324722, A324726.

A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552 by David A. Corneth
isA324726(n) = ((2*n)==bitor(2*n, sigma(n)));
isA324723(n) = if(n>1,isA324726(A156552(n)));

isA324723(n) = if(1==n,0,my(t=2*A156552(n)); (t==bitor(t,A323243(n)))); \\ Using also code from A323243.

cp's OEIS Frontend

A324652 Numbers k such that A318468(k) (bitwise-AND of 2k and sigma(k)) is equal to 2k.

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A324727 Odd numbers such that 2n is equal to A318466(n), bitor(2*n,sigma(n)), where bitor is A003986.

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A324723 Numbers n such that bitor(2*k, sigma(k)) == 2k, where k = A156552(n).

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cp's OEIS Frontend

A324652 Numbers k such that A318468(k) (bitwise-AND of 2*k and sigma(k)) is equal to 2*k.

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A324727 Odd numbers such that 2n is equal to A318466(n), bitor(2*n,sigma(n)), where bitor is A003986.

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PARI

A324723 Numbers n such that bitor(2*k, sigma(k)) == 2k, where k = A156552(n).

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Author

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PARI

PARI

A324652 Numbers k such that A318468(k) (bitwise-AND of 2k and sigma(k)) is equal to 2k.