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

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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)));

A259240 Least n-gonal number greater than 1 such that sigma(n) is also n-gonal.

Original entry on oeis.org

36, 81, 590, 5286126, 15880, 1932821, 37990539325, 6280, 234222782808, 3350529, 931738, 455621651099, 3312, 2680, 373569353, 1128231876, 47531850550, 601657, 4609261, 115668, 164642040082433296, 336577944, 40161257476, 5031720, 31424211, 25785, 12670237746
Offset: 3

Views

Author

Michel Marcus, Jun 22 2015

Keywords

Examples

			For n=4, 81 is a square and sigma(81)=121 is also a square.

Links

Crossrefs

Cf. A000203, A008848, A083674.

Programs

  • PARI
    a(n) = {k = 2; while(! ((p = k*((n-2)*k-(n-4))/2) && ispolygonal(sigma(p), n)), k++); k;}

Extensions

a(23)-a(29) from Hiroaki Yamanouchi, Sep 26 2015

A364131 Numbers k for which A348717(k) is a multiple of A348717(sigma(k)).

Original entry on oeis.org

1, 2, 4, 9, 16, 25, 64, 81, 289, 324, 400, 484, 729, 1681, 2401, 3481, 4096, 5041, 7921, 10201, 15625, 17161, 27889, 28561, 29929, 39204, 65536, 83521, 85849, 146689, 262144, 279841, 458329, 491401, 531441, 552049, 579121, 597529, 683929, 703921, 707281, 734449, 829921, 1190281, 1203409, 1352569, 1394761, 1423249, 1481089
Offset: 1

Views

Author

Antti Karttunen, Jul 11 2023

Keywords

Comments

Conjecture: All terms apart from a(2) = 2 are squares.

Links

Crossrefs

Cf. A000203, A008848, A023194 (subsequence), A348717, A350072.

Programs

  • PARI
    A348717(n) = { my(f=factor(n)); if(#f~>0, my(pi1=primepi(f[1, 1])); for(k=1, #f~, f[k, 1] = prime(primepi(f[k, 1])-pi1+1))); factorback(f); }; \\ From A348717
isA364131(n) = !(A348717(n)%A348717(sigma(n)));
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