cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A351448 Odd numbers k for which A003958(sigma(k)) = 2*A003958(k), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

Original entry on oeis.org

8181, 400869, 1507005, 3918213, 11151837, 22002273, 26669007, 47319957, 58170393, 73843245, 75825981, 83488077, 94338513, 108277641, 119656197, 126889821, 137740257, 163057941, 184758813, 191992437, 199226061, 202842873, 204768225, 220926933, 228160557, 258457473, 264328677, 277602471, 300496797
Offset: 1

Views

Author

Antti Karttunen, Feb 12 2022

Keywords

Comments

Odd numbers k such that A351442(k) = 2*A003958(k).
Any hypothetical odd term of A005820, if such a term exists, should appear in this sequence, in A347391, and in A016754 (odd squares).
None of the first 33 terms is a square, and all of them except 75825981 and 204768225 are multiples of 81. Note that 81 is one of the terms of A008848 (and of A231484), squares whose sum of divisors is also square (with A000203(81) = 121).

Links

Crossrefs

Odd terms in A351447.
Cf. A000203, A003958, A005820, A008848, A016754, A231484, A339905, A347391, A351442.

Programs

  • PARI
    A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
isA351448(n) = (n%2 && (A003958(sigma(n)) == 2*A003958(n)));

A353634 Nondeficient numbers k such that phi(k) = phi(sigma(k)) and A003958(k) = A003958(sigma(k)).

Original entry on oeis.org

234728, 280904, 461168, 463112, 604136, 742664, 909872, 996008, 1065896, 1191944, 1204424, 1224392, 1465256, 1527656, 1620008, 1757288, 1758536, 1956848, 1985672, 2081768, 2102984, 2358824, 2376296, 2405552, 2518568, 2543528, 2589704, 2670824, 2820584, 2899208, 2912936, 3014024, 3151304, 3196232, 3374696, 3432104
Offset: 1

Views

Author

Antti Karttunen, May 04 2022

Keywords

Links

Crossrefs

Intersection of A023196 and A353635.
Cf. A000010, A000203, A003958, A006872, A062401, A351440, A351442, A351446.

Programs

  • PARI
    A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
isA353634(n) = { my(s=sigma(n)); if(s<(2*n),return(0)); ((eulerphi(s)==eulerphi(n)) && (A003958(s)==A003958(n))); };

A353635 Numbers k such that phi(k) = phi(sigma(k)) and A003958(k) = A003958(sigma(k)).

Original entry on oeis.org

1, 26, 74, 122, 146, 314, 386, 554, 626, 794, 842, 914, 1082, 1226, 1322, 1346, 1466, 1514, 1754, 1994, 2186, 2306, 2402, 2426, 2474, 2642, 2762, 2906, 3242, 3314, 3506, 3746, 3866, 3986, 4034, 4274, 4682, 4946, 5114, 5186, 5594, 5714, 5834, 6122, 6434, 6506, 6626, 7034, 7466, 8042, 8114, 8354, 8522, 8546, 8714, 8882
Offset: 1

Views

Author

Antti Karttunen, May 04 2022

Keywords

Comments

Question 1: Are there any odd terms after the initial 1?
Interestingly, most of the terms seem to belong to a set where the abundancy index (ratio sigma(n)/n) converges towards 3/2. But there are exceptions, see A353634 for example.

Links

Crossrefs

Intersection of A006872 and A351446. A353634 lists the nondeficient terms.
Cf. A000010, A000203, A003958, A062401, A351440, A351442.

Programs

  • PARI
    A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
isA353635(n) = { my(s=sigma(n)); ((eulerphi(s)==eulerphi(n)) && (A003958(s)==A003958(n))); };
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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