A340077 -id:A340077 - cp's OEIS frontend

A339880 Odd composite numbers k such that A053575(k) [the odd part of phi] divides k-1.

15, 51, 85, 91, 255, 435, 451, 561, 595, 771, 1105, 1261, 1285, 1351, 1695, 2091, 2431, 2465, 3655, 3855, 4369, 4795, 5083, 5151, 5383, 6601, 6643, 6735, 7051, 8245, 8481, 8695, 8911, 8995, 9061, 9605, 10585, 11155, 13107, 15051, 15211, 16405, 16705, 17733, 18721, 19669, 20451, 21845, 22359, 23001, 26335, 28645

Offset: 1

Antti Karttunen, Dec 24 2020

nonn

No common terms with A016105. See A339870 for the reason. - Antti Karttunen, Dec 26 2020

Antti Karttunen, Table of n, a(n) for n = 1..1237

Cf. A000010, A000265, A016105, A053575.
Subsequence of A005117 and of A339879, and of A340077.
Cf. A339869, A339870 (subsequences).
Cf. also A002997, A053576, A339817.

A000265(n) = (n>>valuation(n, 2));
isA339880(n) = (bitand(n,1)&&(n>1)&&!isprime(n)&&!((n-1)%A000265(eulerphi(n))));

A340076 Positions of ones in A340075.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 11, 13, 17, 19, 23, 26, 29, 31, 37, 39, 41, 43, 47, 53, 55, 59, 61, 67, 71, 73, 78, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 138, 139, 149, 151, 157, 163, 167, 173, 179, 181, 182, 191, 193, 195, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 259, 263, 269, 271, 277, 281, 283

Offset: 1

Antti Karttunen, Dec 29 2020

nonn

Subsequence of A340150 from which this differs for the first time at n=98, as this lacks the term 445 which is present in A340076.

If one applies prime shift (A003961) to each term, and then sorts the results into the ascending order, one gets A340077.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A340075, A340077.

Subsequence of A340150.

isA340076(n) = (1==A340075(n)); \\ See A340075 for the other needed code.

A340091 Odd numbers k such that A064989(k) is in A340151.

Original entry on oeis.org

679, 703, 1387, 1729, 1891, 2047, 2509, 2701, 2821, 3277, 3367, 5551, 7471, 7735, 8119, 8827, 9997, 10963, 11305, 12403, 13021, 13747, 13981, 14491, 14701, 15841, 16471, 17563, 19951, 21349, 21907, 21931, 22015, 23959, 24727, 25669, 26281, 27511, 28939, 29341, 31417, 32407, 38503, 39091, 39831, 39865, 40501, 41041

Offset: 1

Antti Karttunen, Dec 31 2020

nonn

Sequence A003961(A340151(i)), for i >= 1, sorted into ascending order.

By definition, this has no common terms with A340077 nor any of its subsequences like A339869 or A339880.

Antti Karttunen, Table of n, a(n) for n = 1..3290

Cf. A002997, A003961, A339869, A339880, A340077, A340151.

Cf. A340092 (Carmichael numbers in this sequence).

A000265(n) = (n>>valuation(n,2));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A339904(n) = A000265(eulerphi(A003961(n)));
A340075(n) = { my(u=A339904(n)); u/gcd(A003961(n)-1, u); };
A247074(n) = { my(f=factor(n)); eulerphi(f)/prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); }; \\ From A247074
A340149(n) = A000265(A247074(A003961(n)));
isA340151(n) = ((1!=A340075(n))&&(1==A340149(n)));
A064989(n) = { my(f=factor(n)); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f) };
isA340091(n) = ((n%2)&&isA340151(A064989(n)));

cp's OEIS Frontend

A339880 Odd composite numbers k such that A053575(k) [the odd part of phi] divides k-1.

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A340076 Positions of ones in A340075.

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A340091 Odd numbers k such that A064989(k) is in A340151.

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